Sounds like you have a break in the mainline or system line and are sucking in sand or dirt into the line, thus clogging the heads. Start with the furtherest heads and shut or cap off working back to your water source, waiting and watching each time for a puddle, wet spot or a swelling in the lawn. That's where your break is.
Richard Kersten
S&R Sprinkler Systems and Landscaping, Inc.
Destin, Florida