Should I leave my road bike tires inflated all the time ?

Yes, generally you can leave them inflated.

If you have tubular (singles) tyres on your race wheels, which you may have pumped up to 200psi....probably a good idea to deflate after the race.Yes, Why not.
Yes - if you deflate them before storing the bike, then the tyres (and their inner metal cords) can become deformed semi-permanently in the shape formed when the weight of the bike presses down on them. This is why you should never leave a motor vehicle on its tyres if you are going to store it for any length of time.
why not? Do you think they might get overstretched?

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