If De Rossi 6 months coaching took Roma to the lime light, and they were able to finish among top four this season, then maybe Roma might decide to keep him to see if he will do better next season. If he is a coach that can study the players very fast, then it will be of a help to him, but if he is the slow type, it will be difficult for him to adapt fast. De Rossi should try and come up with a play pattern that will be able to withstand the strong clubs, so that he will be able to use that as an advantage, if not, it will be difficult for Roma to challenge these clubs. Let's see what he has for the club during this time in Roma. If he is loved by the players, it will be easy for him.
Roma management has set a target for De Rossi to be able to finish in the top 4 of the final Serie A standings so that they can qualify for the Champions League next season, I think that is a little difficult because currently the competition for the top teams in Serie A is quite fierce, plus De Rossi is not an experienced coach to be able to revive Roma's performance, which has slumped slightly this season.
Of course, if this target is not achieved, it is very likely that De Rossi will be replaced again and I am sure that will happen, considering that De Rossi is not an experienced coach and in my opinion he does not have the capacity to coach a team as big as Roma.