That is how my last battery failed. Check your battery charge voltage with the engine running ~3500 RPM.... I found out why my battery likely failed in that the charge voltage was over 15.5V - voltage regulator was bad and basically wasn't doing much in the way of regulating anymore.
It worked great right up until the point that it wouldn't work any more. It had enough integrity to light the idiot lights with the key on for the first 1 or 2 times of the starter, then voltage dropped below 10V and stayed there until allowed to rest for awhile.
A tell-tale with a bad battery/low voltage situation is observing the tachometer windup to thousands of RPM when the engine isn't running or even turning over - the solid state ignition is trying to come up to voltage, and failing because the battery isn't capable of producing the fraction of an amp it needs to get the electronics to their steady state, waiting for the trigger pulse from the crank sensor. Thus, the voltage at the coil (which is where the pickup wire for the tachometer is) undergoes alot of low voltages pulses in rapid succession - it doesn't take alot of voltage to run the tachometer, so it registers those pulses as the engine speeding up to 7K RPM. Usually it then collapses as the battery refuses to even give the small current anymore and it all sits still, dead. After given some time to rest/recover, it may be possible to get it to do the same thing over again. Repeat until you replace the battery...
