Has any of you ever had a project where you used a pump in continuous operation for weeks and if so, what pump did you use? Any tubing recommendations?
I doubt there is all that much force on the tube after reading how it works, it's more likely a result of overuse, is it designed for continuous use? E-mail Adafruit and ask that question.
Life has a lot to do with the tubing, some types can get old and become stiff and then break much easier. I highly recommend you follow @sonofcy suggestion and contact the vendor.
The picture shows that the pump is easily disassembled and the tubing can be replaced. Ask a tubing source company for a tubing suitable for your project. What is the temperature of the liquid?
Chem labs use Pyrex glass tubing. Art studios use a Bunsen burner to create any shape with Pyrex. Pyrex holds up to major use, like a filled bubble tray with an inverted funnel 2/3 full of "air" and 1/3 full of the reaction of eggshells and hydrochloric acid. When oxidized, the funnel tries to escape the bubble tank NOW, but the funnel tip restricts airflow into the funnel, stoping pressure equalization, so through adhesion, the funnel just holds on to the water and the tank, and everyone launches one meter in the air... and the return to Earth is just as spectacular. No Pyrex broken. Heard it from a friend.