As I know using Rinnengan reviving jutsu only cost massive amount of chakra. The user will not die if he is in perfect healthy condition. Pain case is different where he use it when he doesn't have enough chakra.
If obito could use it on Rin just after Nagato die. It will save him a lot work and time. If I am obito I am sure revive the person I love the soonest.
The only reason I could guest, is that jutsu only can revive those who been killed by Rinnengan owner. Just like Nagato case, he only revive those thing and people he kill/destroy.
And here I guest madara killing himself while he still have the Rinnengan with him aged ago. That's why he could be revived.
However the jiraiya case remain mystery, why everyone killed by Nagato is revived, but only jiraiya remain dead? 2 possibility, 1- not enough chakra or life force. 2- jiraiya is already revived and he is now hiding somewhere or doing something mystery. Will be coming to save naruto soon.