No matter how many times I call, I can't get through.

Literal

How-much phone-call [obj-を] place-[even-ても], don't-get-through.

いくら~ても is the familiar concessive pattern. 通じる ('to get through, to be understood, to connect') in its phone sense means 'the call goes through' — the connection succeeds. In other contexts it can mean 'to be understood (of language)' or 'to lead to (of roads).' 通じません is polite-form negative. A short, practical sentence learners will recognize from real-life frustration.