My impression is that Rodgers sees - or certainly saw - something in him: he was used a lot in pre-season, and started the first European game, in Gibraltar. By most accounts, though, he was noticeably poor in a very poor team performance - maybe partly nerves and partly being used in a position, coming in off wide left, that's not his best. That probably didn't help his chances, but nevertheless, although he's been on and off the bench since, there was no talk of him going on loan in August, whereas apparently Mackay-Steven and Armstrong would both have been encouraged to go had the deals been right.
The biggest problem he's got, as people have pointed out, is that he's competing for places in the area where Celtic are by far at their strongest. Rodgers obviously was under pressure to deliver results and impressive-looking signings straight away, and went for Sinclair, who justified his faith immediately and is an obvious starter given the level he's played at; Rogic is a bit ahead of Christie in terms of time spent with the squad and Celtic first-team games, and he's looked very comfortable in the number 10 role; and players who might have been expected to leave, like Forrest and, apparently, in the last month, Armstrong especially, seem to have had a new lease of life under Rodgers. Rodgers is on record as having said that since the Armstrong loan deal fell through, he's realised that Armstrong's best position is as a number 10; this is potentially bad news for Christie, as he's now got at least two direct competitors for his best position. Things move fast in football, so having been in the plans in August, it may be that come January, he will be advised to go on loan - and he should probably go.
BTW, while I think he's easily talented enough to make it at that level in the longer term, I'm not sure if the English Championship in the second half of the season would be the best place for a player who is still quite young and lacking competitive match practice - the pressure could be absolutely enormous if he's at a team at either end of the division, and it might not do his confidence any good if things don't go well. If they are facing competition at the top of the Scottish Championship, however, I could see possibly see Hibs going for him, given the Lennon-Celtic connection; a step down, for sure, but it would potentially keep his profile high in Scotland and allow him, potentially, to be a player who makes the difference.
Whatever happens, I really, really hope that before the end of this season, he's back playing regularly somewhere - it would be awful if such a talent was allowed to dwindle.