Bt freestyle 350 missing calls?

When someone calls, the phone(s) ring once and automatically answer the call. The person calling hears a mix of silence and electrical static noise... At the same time, person in the house ignores the call as they think the person calling has rang off.
Open reach engineers says there is nothing wrong with the telephone line, all handsets have new batteries and we have depowered the base station without any success. This is an intermittent fault that makes fault finding very hard... Any suggestions?

Popeye
March 2014