*Be sure to read about the Optima Yellow Top and the Priority Start Module. They can also save you some hassles. But this is really the best single intervention you can buy.
The problem is so well known that it has it's own name in the Corvette world : DBS [Dead Battery Syndrome]. I went about 1½ years before my first episode of DBS. If you want to keep your Vette, there are a few things you can do to help the situation.

It is a battery monitor. You attach it to your battery, and it continually monitors the battery voltage. Each time you start the car, it monitors the "cranking ability" of the battery. I'm guessing that means that it monitors the peak number of amps (current) that the battery generates during a startup attempt.
If either the resting voltage or the startup amps fall too low, the Battery Bug © wlll start to beep. This warns you that your battery is getting weak, and either needs to be charged, or completely replaced.
Therefore you know before the battery goes dead that you're in a danger zone. This gives you plenty of time to fix the situation before you're left stranded somewhere.
Whatever the source of the Corvette's mysterious current drain, it's pretty clear that there is one, and that no one will ever be able to fix it. Of the Vette owner's I've talked to, we all agree that if you ever leave the car sit for more than 2 days, you have to put it on a Battery Tender© . With the Battery Bug installed, I don't have to wonder if the car is going to start any more. It reliably starts beeping if I've let the car sit too long, and then I just hook it up to my charger.
For me this is truly THE ANSWER to the Corvette DBS curse. Unfortunatlely, the Priority Start module is a good idea, but I have had at least two instances of DBS occur even with the PS module installed. So, although I do recommnend the PS, it's obvious that the PS alone is not going to save you.
Here are some basic facts about batteries that you need to carry around in your noodle.
Only 1.5 Volts separates a fully healthy, charged battery from a fully dead one! Directly from the Battery Tender©'s owner's manual:
' ...a fully charged 12-Volt, lead-acid battery will have a rest state, no-load voltage of approximately 12.9 volts. A fully discharged 12-Volt, Lead-Acid battery will have a rest-state, no-load voltage of approximately 11.4 volts. That means that a voltage change of only 1.5 volts represents the full range of charge, 0% to 100% on a 12-Volt, lead-acid battery. Depending on the manufacturer, and the age of the battery, the specific voltages will vary by a few tenths of a volt, but the 1.5-volt range will still be a good indicator of the battery charge %."
If a battery is allowed to fully discharge (like down to 10% of the fully charged state), it may never be able to hold a full charge again. This means if you really allow your standard (SLI) battery to go totally dead just one time, you may never be able to fully charge it again. In contrast to an SLI battery, a "Deep Cycle" battery is specifically made to withstand total discharge, and still perform normally after it is recharged. "Deep cycle" Batteries like Oddyssey and Optima can withstand somewhere in the range of 2000 total discharge / recharge cycles.
There are two different types of batteries
The bottom line here: yes, you want a Battery Bug©, but you also need to choose a deep cycle battery to go with it. Although an Optima or Odyssey may cost $200, it's better than paying for a new battery every time your Vette allows a deep discharge of your standard battery.
If there is no alarm situation, the display continuously cycles between the battery voltage and the cranking health % (see picture above). You're in good shape as long as the cranking health is above 30%, and if the voltage is ≥ 12.2 Volts.
For me, this second point is the real key to life. If my car is in the garage for 4 or 5 days, the voltage will drop to 11.9 or 11.8 volts, and then the alarm will go off. I can plug the Battery Tender in overnight, and the situation is fixed before I go to work the next day.
Read more about the Battery Bug©: [Model #BB-SBM12]
There's no need for any photos or details here. See the photo. The device is just a small monitor with an LCD screen. All you have to do is stick the monitor on the side of the battery to hold it secure, using 3M tape. Then attach the red and black electrical leads to your battery's positive and negative terminals. That's it !
It might be helpful to know that Argus makes many battery testers and analyzers. The model we're discussing here is labeled "BB-SBM12."
At this point, you shouldn't be paying more than $40 for this, but like I said, you can probalby get one at Griot's for $30.
Some day, GM will make a Vette that can hold a charge as well as my 1980 Volkswagen Rabbit. But that day doesn't seem near. Until then, you need a Battery Bug© to keep you safe. For $30 and a two minute installation using a couple of wrenches and a piece of 3M adhesive, you'd be insane not to have one of these.
Now if only I were paid for this advertising...