It's the battery. Car batteries don't hold up, the lead plates break up and short due to hitting double ups and sulfate because they rarely get fully charged.
Here's how you check: Get a digital multimeter, they're cheap these days. Set it on DC volts, check the battery voltage with the boat not running. A fully charged battery should read about 12.7 VDC. Start the boat, read the battery voltage at the battery terminals while it is being charged. If the alternator is working, it should read higher than the battery did by itself, usually about 14.5 volts. That means your alternator works. You could check the battery over a couple of days, it will drop a volt or two over time. Easy thing is to take it out and take it to an auto parts store for load testing.
You can jump your epic with a good battery and remove it while the boat is running, I've done it. I now carry a jump starter ($50) from west marine, and have 2 batteries.
I would recommend replacing it with an Optima, they won't fail as quickly and will hold a charge indefinitely. They are not a direct retrofit for the series 58 that is in the boat stock, I cut out part of the lip on the driver side of the battery hole to fit one in my boat. I settled on a NAPA series 58 starting battery (stock size and location) and added an Optima deep cell and an isolator to run my stereo, see the how to page.
Good luck, if you need more help, let us know!
Pete