We have Verizon and never had any problem like that.

Have you had you house connections and street connections checked ?
or is it something in the Verizon lines in your area?
Do other neighbors have the same problem or only your house?

That would tell you if it is the Verizon lines or possibly the connections for your home only.

You can do a visual check of your wires & phone line connections that show above ground.
Do any look like water could be causing a short or something?

for the rest of it Verizon should come out and do a check for you.

If someone dug near the line underground maybe it was nicked..??
Just enough so when it rains it has a problem???

ours runs under and across our driveway so we kind of know where it is in general.

wired /plugged in?? or wireless and lose the wireless connection?