it all depends on how he and the team finishes out the season.
if the team is winning (esp. against the broncos, MNF, and against division rivals) , if the coaches are calling the game better and are making necessary adjustments, and if the players are grasping the system and are responding well to rivera & co, then yes, they should be staying.
the next half of the season is going to be what decides their fate, imo, and i hope they do well. i don't want the team to go through another rebuild. i'd rather this current group be able to work.
Not every new coach has to rebuild. More or less this team just needs to be recalibraded not rebuilt.