You make a transaction, it gets included in a block, and now has 1 confirmation.
When the next block is mined on top of the one containing your transaction, it has 2 confirmations.
On average, 6 extra confirmations will be generated per hour (144 per day, 1008 per week, 52560 per year) , forever.
Offcourse, some services might chose to show only the first couple confirmations in their GUI, this doesn't mean more confirmations are added
So basically it stay forever and never stop unless Bitcoin dies with one way or another . thanks !