Most likely to be a vapour lock in the tank due to a blocked vent. Next time it happens try opening the tank filler cap. If you get a whoosh of air, the problem is in the tank.

 

Agree with the cap venting.

Also the pump may be getting tired, and the diaphragm is simply not up to the task.

Insulating the pipes will do no harm, and I use a product called "header wrap", which is foil covered fibre that works extremely well.

The 25c+ is not so hot. We get 45c+ here and my S Type (1964) never had issues at all.