I've been following this thread for awhile now and have read some interesting, albeit misguided information regarding batteries in general. I have a few questions/comments about the original post though. After reading a thread posted elsewhere today by the OP, you stated your resto was done 4 years ago. Why would you look any further into a warranty on your battery? The AAB website clearly states their batteries are warrantied for 4 years. Do you know which version of battery your restorer purchased from AAB? They offered Autolite group 24 batteries in standard lead/acid and now in AGM ("maintenance free"), versions. Just to be clear though, BOTH are lead/acid batteries.
The standard life of a lead/acid battery is 3 years...period. Batteries are offered for "longer life" than this, but all you are actually paying for is a warranty (prorated no less!) which covers a greater period. Some batteries last less time, and are cheaper, due to being constructed of cheaper materials. Before anyone pipes up and posts about their battery lasting X number of years longer, you're absolutely correct. I have the factory original Motorcraft battery in my truck that's now 11 years old. ANY time after 3 years is simply "borrowed time". It's been helped along though through proper maintenance.
Now to clarify a few myths. AGM batteries ARE lead/acid batteries. They have lead plates and are filled with sulfuric acid as the electrolyte. Some of the differences between them and a standard lead/acid battery are:
1) There is less acid in an AGM battery
2) AGM batteries are not free venting. This is notable for restored cars because there is less corrosive vapors emanating from the battery which could cause damage/corrosion. Take note I said LESS venting. AGM batteries have a vent and DO vent. The vent is a one way pressure relief design though, as opposed to a "free air" vent in a standard lead/acid battery. If a lead/acid battery was not vented it would develop enough gas pressure from recharging to rupture the case. AGM's vent VERY little though due to the design and amount of acid in them.
3) AGM batteries are less prone to failure due to shock (physical not electrical), and vibration.
The discharge rates of standard and AGM batteries is very similar. The RECHARGE rates are different though, with a greater recharge period required for an AGM. They CAN be recharged, they CAN be kept on a float charger and they CAN be jumped. There are no magic hocus pocus electronics inside them either. I've read through some of the claims that manufacturers make regarding their products, batteries and chargers alike. Optima claims up to 5x greater battery life. Over what?! A cheap battery? Sure, they use better materials. Battery chargers can vary, but it's in how much and how high a charge rate is delivered and over what duration. Reading through some claims is like reading a snake oil bottle. If you know about batteries and the chemistry involved you can quickly read through the contradictions or "better than" claims in order to see they are functioning as any good charger (constant or float), should.
A VERY basic explanation of how a lead/acid battery works is as follows; lead plates are suspended in a non-conductive acid proof case. There are two sets of plates with non-conductive separators between them. One set of plates is the anode and the other the cathode (positive and negative sides). The lead is not a plain piece of lead. It's a specific type of porous lead known as sponge lead. The electrolyte is sulfuric acid (H2SO4). The chemical reaction between the electrolyte and the lead plates creates an electrical charge (voltage). As the charge is created and used, the resulting reaction (basically) draws the acid out of solution and into the plates. If you were to measure the pH of new sulfuric acid and then compare it to a fully discharged battery, you would see a lower pH in the the discharged battery. That's because your reading (again, basically), is water. When the battery is charging the electrical input TO the plates forces the acids back into solution. Basically it "mixes, if you will, the acid back into the water. A byproduct of this charging reaction is the formation of gas, hydrogen gas to be more specific, and vaporization of some of the water. When the water is vaporized through charging, there is less "solution" for the acids to be forced back into and it remains in the plates. That's why after initially filling a new (non-AGM) battery with sulfuric acid you only top it back up with straight water. You are replacing what was lost....water. Through time salts will remain on/in the plates. This is what sulfation is. It is also UNAVOIDABLE. PREMATURE sulfation can be avoided with proper maintenance. AGM batteries are not as prone to it either due to their design/construction. The other thing that eventually kills a battery is deterioration of the lead plates. As they deteriorate through use/time they slowly break down, forming a lead "sludge" (for lack of a better term), in the bottom of the case. This "sludge" can build to the point it comes in contact with the bottoms of the suspended plates. The plates are then shorted out, effectively "killing" that cell. That, in a nutshell, is a VERY simplistic explanation of how a lead/acid battery functions.
Another thing I'd like to mention is charging. Fast charging is harmful to the life of a battery.....ANY battery. It increases the chemically induced deterioration of the battery. It also boils off the electrolyte. This is HIGHLY critical in an AGM battery due to it having less electrolyte in it. Keep in mind also it increases the formation of gas...hydrogen gas. Which is, if you remember your high school chemistry class, HIGHLY explosive! With a charger attached via clamps, NEVER remove the clamps from the battery before unplugging the charger first. The resulting spark could ignite any hydrogen gas lingering. Prolonged constant charging can also force the battery into a thermal runaway. Charging causes an exothermic reaction, e.g. generates heat. Just feel the sides of a charging battery. Lead/acid batteries are not as sensitive to it as Ni-Cad batteries are during charge/discharge, but it something to monitor. Again, this is a bad thing, not only for the life of the battery but also for safety. It should be mentioned, always check the fluid levels PRIOR to charging. After charging and a brief cool down period, check and service again if necessary. If a proper charge rate was applied, you should have minimal fluid loss though. Always service with distilled water to avoid chemical/mineral contamination of the electrolyte.
Also worth mentioning is "maintenance free" batteries (excluding AGM or Gel types). Bottom line, they AREN'T! They are free venting just like "normal" lead/acid" batteries. They require the electrolyte to be brought back up. No caps you say? Wrong! If you ever examine the tops of them you'll see a very thin line in a rectangular shape. This is a cover plate that is snapped onto the top. It is removable and will reveal access to the cells. Some cover recessed individual caps for each cell and some have molded on "plugs" along the length for each cell. Simply service the battery and snap the cover back in place. There are a few brands/models that are molded closed and are truly NOT serviceable, but most are.
I know this was a lengthy post, but I felt it was subject that needed to be clarified. If you're interested in HOW an AGM is constructed and chemically reacts (slightly) different than a regular lead/acid battery, just Google AGM battery. Don't go to a manufacturer's page, but a straight reference page. You avoid all the "claims" this way for a truer explanation. I hesitate to mention Wikipedia because some folks feel it's primarily hogwash. There are many reliable reference sites though.
BTW, I spent 15 years as an aviation electrician. Not only did we maintain the electrical systems, but we had to maintain all of the power sources, including batteries (lead/acid and NiCad). As such we received formal training in their construction, maintenance and function. If there's any furthr questions regarding this subject that I can help with, please feel free to ask. If I can provide an answer I'd be happy to help.
p.s. To the OP, it sounds like it's time for a new battery, plain and simple!