It sounds like you're in US [Tarparlin / Tarpaulin] and the roof covering is on its last legs and it's 'popping it's cloggs' ie its had its day.
If the leaks are few then coat with brush or trowel on butumen roof sealant.
If many leaks then long term is its cheaper to re-cover. Aquire 3-4 prices or if you reckon you can then do it yourself. Think on the lines of plastic corrugated roof sheets also. DIY Books around to tell you how, you must have a library near you.
Bob
August 2011
Automatic Answer
We may have found other answers which could help you.
howtomendit.com for free repair help, information and advice.
Try fixfault.com to fix roofing.