Your battery might be on the way out -- some batteries last a long time but others only give you 4 or 5 years at the most. Depends on usage. Infrequent usage can cause a battery to die young. You can get your battery tested at one of the suppliers.
Also get your wiring and connections checked. You may have a bad earth connection -- a not uncommon problem with early Vettes. This can cause sluggish starting even with a good battery.
Another possibility is that the battery is being drained while the car is not being used. C3 clocks can pull quite a bit of current, as can alarm systems. Even some radios with electronic tuning can pull a bit of current keeping the station memory alive.
Many of us use a battery disconnect switch (such as used on boats) when the car is not being used frequently. As well as that, you can use a "smart" battery charger that can be connected to the battery for long periods which will keep the battery in excellent condition without overcharging it. I have a couple of Battery Fighters for that and they are great:
http://www.batteryfighter.com/product.html