Only one ring on incoming calls

We have a landline phone with 3 jacks in the house. Over the last month, we've had problems with noise on the line and no dial tone. A call to Verizon resulted in a tech checking the box outside the home, running diagnostics, indicating that there was no problem there and then the problems correcting themselves (without a tech needed inside the home). Over the last 2 weeks, while we have a clear line and dial tone, we only receive one ring on all incoming calls -- then deadspace. The caller is also only hearing one ring and then nothing. If we run to the phone before the caller hangs up, we get the call. But if not, the answering machine will also not pick up. We unplugged all 3 phones, put them back one by one -- same issue consistently. We contacted Verizon. A test on their end indicted no problem on their wires. A tech came to the house and checked the box outside -- again, no problem. He came in, plugged in his diagnostic phone into one of the jacks and voila! Multiple calls to our number came through with 4 rings -- then the answering machine picked up. He said there was no problem and left. In disbelief I had a few people call and the phone worked. 2 hours later -- the same problem is back: only one ring on all incoming calls.

Any ideas on what could be up? I am hesitant to call the tech again -- and be charged for another service call.