Hi, Anonymous and the usual suspects are:
1. Severely discharged or a damaged battery should have 12.5 volts or more and be able to pass a proper "LOAD" test if necessary, you may have a cursory reading of 12.5 volts or more but little or zero amperage the battery is faulty and must be replaced, AGM batteries fail in this scenario more so than lead acid batteries.
2. Check battery terminals for damage or corrosion, check the battery cables at "BOTH" ends for loose, corroded, or broken connectors, "INSIDE" and outside the cable harness, perform connector wiggle test and check cables with an ohmmeter if necessary.
3. Spark plugs in bad condition or partially fouled.
4. Spark plug cables in bad condition and leaking check for spark leakage in the dark
5. Spark plug gap too close or too wide.
6. Faulty ignition coil, module, and or sensor.
7. Loose, dirty, or corroded ignition module connector at crankcase.
8. Faulty CKP or CMP, MAP, ETS, ATS, TPS, O2 sensor.
9. Dirty air filter.
10. Intake air leak.
11. Water, dirt, or rust in the fuel system.
12. Carburetor contaminated, sticky float, plugged jets.
13. Carburetor vacuum diaphragm torn, cracked, not seated or installed improperly.
14. Multiple carburetors out of sync.
15. Fuel filter clogged.
16. Old or contaminated fuel.
17. Fuel tank vent system plugged or carb vent line closed off.
18. Gas cap diaphragm valve faulty.
19. Vacuum line from intake manifold to fuel valve is broken, cracked, pinched, or missing.
20. Carburetor controls misadjusted.
21. Incorrect valve timing.
22. Valve springs floating, weak, or broken.
23. Damaged intake or exhaust valve.
24. Incompatible performance parts.
25. Control module may be in "LIMP" mode
26. Check for engine trouble codes.
For more information about your issue and valuable "FREE" downloads that you will need please click on the blue links below. Good luck and have a wonderful day.
Honda CX500 Ignition Problems Tech Corner Motorcycle Classics
Honda CX500 Shop Manual
Honda CX500 CUSTOM Owner Manual