I guess the reason why bitcoin has a stable price is because miners are mining sometimes or even stop mining at all. The supply of coins freeze and the price would definitely freeze to. Correct me if im wrong but i really believe mining and the price are linked. If one stop moving then the other one will follow.
You're completely wrong.
Bitcoin miners simply don't go on a hiatus. Even if one miner goes down due to maintenance or whatnot, there are thousands of other pools and individual miners/mining farms that are working round the clock to verify transactions.
Mining simply doesn't pause, and the supply of bitcoin will continue to go up as soon as a new block is mined, even though that has no apparent short term affect on bitcoin prices since the block rewards are so low compared to how many bitcoins are already in circulation.
What makes bitcoin prices stable at this stage is because of the bear market. We're finding a bottom at $5-6k and prices are consolidating, there is nothing related to mining whatsoever.