I used to have an MGA that killed batteries. Lucas=Prince of Darkness, etc. After years of wondering I finally figured out that the back suspesion was so stiff it slammed the batteries hard enough for the lead panes to come loose from their internal morings and short out. If bounced wrong, the battery would be dead. A little wiggle and presto, it worked again.
The cure for my MGA was to buy an off road battery that was designed for heavy bouncing, but I'll bet just a new battery will fix your problem.