[AzTumbleweed]

A weak battery should not make it quit running if you have a good alternator. You have not said whether or not the BATTERY warning light is coming on. This might be a long shot but here's what I discovered on my Escort. The brushes in the alternator wore out. For some reason if it quits charging due to bad brushes the BATT warning light does NOT come on. Typically, it would charge when I started it up but quit charging after a few miles. The only way I knew this was that I have an after-market battery gage. If you have a volt meter I'd lengthen the leads so it would reach the inside of the car then go for a drive and watch the meter. If battery passed load test I'd rule that out but you might go to AutoZone for a second load test just to confirm it's good.