Ok, let's go with that. Hours outside the transporter buffer. Let's say two hours. Suppose he gets down to brass tacks and figures he going to absolutely minimize her time out of the buffer. So, he rematerializes her and then dematerializes her as quickly as possible. No time for games and storytelling. That sucks but it's necessary.
Say she's out of the buffer for 1 second at a time before dematerialization. There's 7,200 seconds in two hours. Even if it he needs to rematerizalize/dematerialize her every day, that's 7,200 days! Even if you assume that it requires 10 seconds outside the transporter buffer each time, that's 720 days or about 2 years. It's not imminent either way.
Furthermore, they didn't even sell the fact that she was so close to death. We didn't see her getting sicker. She just didn't seem that sick.
For me at least, all of the detracted somewhat because his extreme decision of handing her over to a questionable entity didn't seem necessary. Of course, YMMV.