As the title says , I'm wondering if the transactions keep getting confirmations with the time or it stops at a certain time ? If it doesn't stop at all then why exactly ? what's the point
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
EDIT: after some googling, this should have been satoshi's first transaction:
https://blockexplorer.com/block/00000000d1145790a8694403d4063f323d499e655c83426834d4ce2f8dd4a2eeIt now has 406902 confirmations, and counting