Problem started a few weeks after I installed a new battery. The odometer/trip gauge will reset to 0.0 when I turn the ignition off. The problem has gotten worse over time as when it first occurred, it would reset after sitting overnight. Now it resets as soon as I shut the car off. Has anyone else had this issue and found a fix rather than replacing the entire gauge?

 

It's possible you have a bad capacitor on your speedometer circuit board. You can try to repair it yourself by following one of the guides here on the forum or send it off to an electronics repair shop. It probably isn't worth repairing right now, but if the capacitor is leaking it can damage other components on your board.