Sam isn't trapped in time or forced to leap or anything. He willingly chose to continue leaping because his whole character is about helping people.
Dialogue from the final episode:
Bartender:
Why did you create Project Quantum Leap, Sam?
Sam:
To travel in time.
Bartender:
Why did you want to travel through time?
Sam:
Because... I w-w-- I wanted to, um-
Bartender:
To make the world a better place?
Sam:
Of course. To make the world a better place.
Bartender:
To put right what once went wrong?
Sam:
Yes. But not one life at a time.
Bartender:
Oh! I got Mother Teresa here.
Do you really think that all you've done is change a few lives?
Sam:
Basically, yes.
Bartender:
At the risk of overinflating your ego, Sam, you've done more.
The lives you've touched... touched others, and those lives, others.
You've done a lot of good, Sam Beckett, and you can do a lot more.
Sam:
I don't want to do more. I want to go home.
Bartender:
They why haven't you?
Sam:
Because I don't control my future.
Bartender:
You do! Sam, you will only do this as long as you want to.
Sam:
Are you saying I can leap home anytime I want?
Bartender:
Technically, yes.
Sam:
What's the catch?
Bartender:
The catch... is that you have to accept that you control your own destiny.
