Harry
LEGALLY - no. When you enter Thailand, your bike gets a temporary "tourist visa" good for 30 days. After that time, you have to take the bike out of Thailand.
I am not sure about using a Carnet. I know people that have used them in Thailand. But,having a Carnet does not give you more than 30 days.
ACTUALLY - you can PROBABLY get away with it. You could do a "visa run" with the bike when you return for the next trip. That would make it legally in the country for your travels. Or, you could just take it out when you finally leave. Either way, you will probably have to pay a fine.
There are several bikers in Chiang Mai that are doing the same thing now. SO FAR, they are getting away with it. Hopefully, they will post some of their experiences here.
But, this is Thailand. There a a lot of possible scenarios, depending on where and when you take the bike out, or if you have to deal with the police. The Thai system is slowly getting more efficient, and rumors are always flying around about stricter enforcement of the existing laws.
You might consider buying Thai insurance for the bike, and putting the sticker on the bike. The minimum policy is only 650 baht per year, and it would give an image of legality.
Good luck.
BobS