Is it possible to get a service provider , which provide stable, not-changeable BTC address. My new employer prefers Bitcoin as the way of salary payment, but the address keeps changing, is it possible to get a non-changeable on, or is there is any other way to transfer bitcoins from one person without entering new address every time?
With most providers, an address should remain valid indefinitely.  This would certainly be true if you use your own software wallet, instead of relying on an online provider.  If you give your employer one address, they can make transactions to that address as many times as they want, and you'll receive those coins.

It is usually recommended to use fresh addresses for each transaction, because it is better for privacy, and makes it harder for other people to track your activity.  But it isn't required by the Bitcoin protocol.

If your employer (or their payment processor) insists on being given a fresh address for each payment, that is their decision, not a technical requirement of Bitcoin itself; you'd have to take it up with them.