Even with this I would argue that fixed cost would have been the way to go. They were losing $X every day for that six months that it wasn't working. They hired you to fix it, and even if you charge them way more than your day rate you're not solely charging them for the change - you're charging them for "knowing which screw to turn".
The hardest part of getting into contracting was the guilt of feeling "I'm charging too much for a simple fix!". If the fix was so simple and the client didn't find it in those six months then maybe your assumption that the fix was simple and obvious was incorrect. Regardless, your fix provided value, and you should be compensated for the value that you provided, not just the number of hours worked.
The hardest part of getting into contracting was the guilt of feeling "I'm charging too much for a simple fix!". If the fix was so simple and the client didn't find it in those six months then maybe your assumption that the fix was simple and obvious was incorrect. Regardless, your fix provided value, and you should be compensated for the value that you provided, not just the number of hours worked.