The fiends have either been allowed to invade for a time being as punishment for the transgression of some large group of inhabitants of the prime, or else the fiends have earned the right to invade for a time based on some treaty or contract between the fiends and the celestials.
In the first case, the Celestials are awaiting the coming of a Redeemer who will atone for the sins of the group or person who committed whatever horrid sin so offended them. Alternately, they await at least an admission of guilt and a general cry of mercy on the part of the inhabitants of the prime. In other words, saving the prime involves convincing a large percentage of the populace to engage in a sincere act of piety.
A variation on this is that the group was so evil and powerful, that the celestials allowed the invasion in order to premptively destroy the group before it became an even greater threat than the fiends. The celestials are biding thier time to see if the enemy has been destroyed or at least weakened enough to directly intervene.
In the second case, conditions are fairly similar to the first, but the possibilities are more varied depending on what the contract calls for to restore control to the Celestials. A mortal Redeemer may be required, or the Redeemer may have to be a God or Celestial. The contract may specify a period of time (40 months, 40 years, 1000 years) before the Celestials are allowed to intervene. Or the contract may specify that a trial or test must be conducted at some regular interval by champions of the two sides and for some reason the Celestials are losing.
In all cases, the Celestials may be investigating the matter, and secretly working behind the scenes in preparation for more open warfare. In the case of a contract, the more chaotic minded celestials may be breaking both the letter and spirit of the contract - which may in fact be prolonging the legal right of the Infernals to invade, resulting in a situation where the more Lawful minded Celestials are spending more time fighting thier Chaotic brethern than the Infernals.
Naturally, the PC's are destined to assist in setting the matter right, either as the direct actors themselves, or as the comrade of the direct actor (who may not appear to be that extraordinary until the climax).
For instance, I'd be very tempted to start such a campaign with the PC's rescuing an orphaned female human child. This child is actually an incarnation of a diety and is destined to defeat the Arch-Fiend at an appointed place and time (by for instance naming a epicly powerful Holy Word at a particular 'nexus of reality').
The child appears to be a low level commoner through most of the campaign. She attaches herself to the PC's, and always manages to resist being separated. If left with friendly clerics, she runs away and appears at inoppurtune moments, etc.
