I ended up using confirmtx.com
Did not happen automatically within 24 hours, their email support is wrong when you use coinpayments gateway, found the guy on this forum. He said he would check it. It got confirmed some 12 hours later. Wheter it was him or just a random miner picking it up is impossible to tell.
In my humble opinion, this site works just like a site that sells "a rock that protects from tigers". They do nothing, in many cases the transaction will be confirmed, and in the worst case, they can refund the fee.
The scary thing is that the network did not drop it. I would much rather prefer if there was a hardcoded limit when transactions get dropped.
There is no such thing as hardcoded time limit in the distributed system. How you are going to enforce it? There is no common time, everybody sees everything differently. Somebody may see your transaction immediately. Somebody may see it later. The former group may forget about it but the latter will retransmit it. Somebody may store and retransmit the transaction just for fun. And you cannot ban retransmission. Otherwise, you won't be able to make the same transaction again. Moreover, storing a database of already transmitted transactions would by a DoS weak point. Somebody can flood the network and exhaust the memory of the nodes.
The current situation is the best one. Unless somebody double spends before the transaction is confirmed, the transaction should be considered final. Double spending is the only thing that can "reverse" a transaction.