Certainly asking for a warranty after NORMAL job completion if it was not in the contract would be unusual and a bit crass - sort of like asking for ice cream on your pie for free after it is brought to your table.
However, since there were problems that were redone and you are not confident in them, it would be fair, in my opinion, to ask for a written warranty on only those specific items or potential types of failure - 6 months would probably be reasonable, 1 year would probably be the maximum that would be considered - contractor might come back and propose 1 or 3 months so be prepared for how emphatic you intend to be about it, realizing in his mind it has been fixed so is no longer dubious. The type of fix would make a difference too - for instance, if a defective item had been totally replaced he would feel it is a closed issue, if it was just repaired or caulked or redonethe same way that failed initially (like a peeling paintjob) then your position to question it is probably stronger. Also, seasonall factors might come into play on some types of work - for instance, a roof or gutter or window or exterior paint job warranty might need to carry through the winter or the rainy season to be meaningful; interior things except maybe foundation/basement waterproofing and westher stripping and heating/air conditioning systems probably do not have much of a seasonal component to their performance.
Phrasing would just be a statement on the final invoice or a change order or contract amendment like this -
"Full labor and materials warranty on hall bathroom shower against leaks for a period fo 6 months is included" or similar.
I would bring this up with him ASAP at the time you are going over the final punchlist of items to be wrapped up (if you are not already past that point), NOT when he hands you the final invoice for payment, so it comes across as a job completioin issue rather than looking like you are looking for something for nothing at the time of final payment.