Increasing more often, the 95 Honda EX would not turn over as if the battery is weak or dead but it's not. Try a few times and wait a few minutes and it starts. Any one has similar experience?

If what you are describing is just a cranking problem, possible causes are:
1. Corrosion on battery cable, starter motor, or starter solenoid connections.
2. Failing starter solenoid or starter motor.

Disconnect negative battery cable and record any radio code before servicing.

Many auto part stores will diagnose these problems for free.