The only way to start my 125cc scooter is to kick-start. Is it because I am not riding it enough? The button ignition won't work and is usually completely dead.

Ideally you need to get the battery tested – if the battery is flat, then it cannot activate your electric start. If your battery is in good condition then the fault will lay a little further down the line, either with the starter solenoid or the starter motor itself. Either way you must start at the beginning with the battery.

Pete,

Locate the fuse box. Depending on the scooter it is either under the seat or under the side plastic . Maybe you have a blown fuse.

Fuse OK? Check the battery terminals are clean and tight. Unplug and reconnect any plugs in the wiring you can see. This cleans the connections.

Still No go?

It's a system of elimination.

With scooter stopped will the horn work?
No. Battery is dead.

The next bit may not work as some scooters have AC headlights but...
Turn on the headlight and/or turn signals.
Press the starter does the headlight and/or turn signal go out?
Can you hear a click?
Yes.Battery maybe OK but does not have enough charge to operate the starter. If you ride everyday you need a new battery about 600 baht.
No. Then the problem is in the switch, the wiring , the solenoid or the starter.
Press the button and tap the starter with a hammer. Sometimes the brushes are stuck.

Last resort go to the dealer. Cheaper than buying a multimeter to test any further.