If you're renting an apartment, chances are very good your lease requires you to go through the building manager for all work and won't reimburse you for the costs - or even legally prevents you - from using another roofing contractor. You may be stuck with working with the building manager.
Tell the building manager the number of times the roofer has failed to fix the roof; that should indicate to him/her to find another roofer, since the roof keeps failing and it's costing the building owner a lot of money, damaging your living space and possibly causing damage to other parts of the building.
It is possible to contract the repairs yourself with a roofer you choose and deduct the costs from your rent. Pennsylvania has a law called the "implied warranty of habitability" that ensures that tenants have safe and decent housing. This means that every landlord in Pennsylvania must make the repairs needed to keep the rental housing in a safe, sanitary and liveable condition. See PALawHELP.org - Your Online Guide to Legal Information and Legal Services in Pennsylvania.
But don't schedule repairs until you read that site and talked to PALawHELP. And if you go that route, be sure and follow the correct process to notify the landlord beforehand, be prepared to show documentary evidence (photographs, dates of previous repairs, etc.) of the damage and the completed repairs, and also realize the landlord could still sue for you for non-payment of rent when you deduct the costs if the landlord thinks the costs were too high.
If in Philadelphia, also see Tenant Union Representative Network; they have free TURN workshops weekdays at 12:30 p.m. or on Wednesdays at 5 p.m. and can answer questions about repair/deduct process and probably help you with it and working with the building manager (but not in the capacity of a lawyer).