The ballast'' is'' causing your problem, and it can be changed. You need to remove the original ballast, (after you shut off the circuit breaker) and take it to a lighting place or electrical supply house. Better yet, get the numbers off the ballast first and call. It may take them a little while to cross reference the part number, but they will find you a suitable replacement.
With any luck, the replacement ballast will be the same size as the old one. If it is not, you will need to find a way to secure it to the old fixture. Perhaps you will need to drill new pilot holes and use sheet metal self tapping screws. Rewire the light if you have to, plug in the new ballast, reset the breaker and you should have bright consistent light.
Otherwise, for a few dollars more, you can get yourself a new light fixture