not infinite time
I had a long complex itinerary to book, waiting for each flight date - 330 to hit to snag award seats. You have some time as courtesy hold, but not an extraordinarly long time -- a matter of weeks IIRC. Then you can get it extended but the process involves rebooking each segment, so if any one of them no longer have award availability, you need alternate flights or are just out of luck. I stretched a few times until the awards ran out, then I had to lock it down and ticket or lose the whole thing.
This can be a nerve-racking part of booking a 3 or more week award itinerary. I did a 6 week OW trip several years ago that really pushed this to the edge; my most recent is a 3 week jaunt through the Americas next summer, the one where I hit the rebooking inventory issue while still hoping to optimize some elements of the trip.
once ticketed I can still look for more convenient times and even dates but can't change any destinations or sequencing. Well worth it given the amount of travel in premium cabins you can cram into a relatively low-mileage award.