EPDM has a problem forming attachments--not only with other things, but attachments between sheets of EPDM. The EPDM sheets on a roof must attach to each other and must also fit around pipes and other fixtures that sometimes have unusual shapes. They are two major causes for for EPDM working loose: it was improperly sealed in the first place or the cumulative effects of ultraviolet (UV) radiation causes the sealant to dry out and crumble. Making sure that the EPDM was installed by competent professionals is the cure to the first problem, and covering the EPDM with gravel or some other (preferably light colored) material solves the second problem. Unfortunately, EPDM is always sold in black sheets, which is the worst color for preventing UV damage.
Tenting is when the EPDM becomes unattached from the roof and billows up in "tents." This problem is a precursor to other, more serious problems. Once tenting occurs, the EPDM is easier to puncture and pools of water are easier to collect. Sometimes, tenting is caused because there is a drainage problem with HVAC systems, which often vent to the roof. The HVAC exhaust systems can become clogged, which can cause steam vents to expel the super heated water that causes the EPDM to tent. Checking to make sure that all the rooftop systems are working correctly should be a regular part of building preventative maintenance schedules.
There are two main caused of punctures: birds and people. Keeping birds off a flat roof can be accomplished in a number of ways including statues of owls and alarms that birds dislike. The best way to prevent punctures by humans is to install raised walkways that go to all the places that humans need to check.
The other major use for EPDM (besides roofing) is as pond liners. They work well for this and are certainly an improvement over the previous favorite, PVC lining. EPDM lasts longer then PVC and it is not harmful to fish. Because the EPDM is underwater it does not suffer the UV degeneration that is common with roof EPDM, and because it does not have to accommodate pipes and other features, there are a lot fewer seams to work loose. There is, however, one major problem: Unless the pond is very small, the EPDM sheets must be attached to each other. If not done by a competent professional, these seals will come loose and the pond will leak.