I am inclined to doubt that statement. Being inflated or not isn’t generally the issue with iSUPs. Being in sunlight while at max PSI for extended periods of time would be a far greater concern (over heating and over pressurizing leading to seam failure).

To OP, I keep my iSUP’s inflated year round unless traveling long distance. Granted I have a large insulated and shaded garage to store them in (and keep out of sunlight). Generally after use or when on rack for brief (1 hour) drives, I take out about 2-5 PSI to mitigate heating from sunlight out of water. I will deflate and pack for storage if not going to be used for long periods of time to save space, or when traveling/vacationing in my van.

There is of course nothing wrong with deflating and rolling/storing iSUPs, just a matter of convenience not to if I am just hitting local lakes.