Flat tire from indoor trainer

I have a Bianchi Volpe with 32 wide rims. Four times I have brought it into the house, take the front wheel off, put in on the trainer and work a bit. When I come back the tire is flat. The tube has a slit about 1 inch long. The tire says 58 psi and 87 psi maximum. I use 80 psi. Please help me. I am going crazy.
Jellymuscles

 

Is it the front wheel that is blowing out? Sometimes there is enough clearance between a certain rim and a certain tire that allows the tube to push out a little between them. Eventually you will get a blowout like this. I had the same situation with a Panaracer tire on a Wolber rim. Since I was riding the same size tires on the front and back, I switched them and all is well now.

 

Check out what the previous poster said. I would add that sometimes the same hole on a tire is responsible for several flats, even if you had previously pull out any debris off the hole. Just replace the tire for a new one and see what happens.