Vittoria Corsas - do I need to keep them inflated in off-season?

Vittoria Corsas - do I need to keep them inflated? I have a pair on a set of race wheels which I used at IM FL and probably won’t use again until May. As is typical with these tubulars, they do not hold their pressure for more than a day or so. I have been told by my local bike shop that to keep the tires from pulling away from the rims I should keep them inflated - which means I’ll have to pump them up every night (don’t think this is gonna happen). So, what is the downside if I don’t keep them inflated? Is LBS correct? Or, along about May, can I inflate them and see what happens? Or, in May do I peel 'em and re-glue 'em?

No need to keep them inflated. Tubulars should be reglued at the beginning of each season, whether they need it or not.

No need to keep them inflated IMO.
There are also the new Vittoria Triathlon tubulars that according to Vittoria do not leak as much as other tubulars.
Sergio