Hey Alessandro,
>> "If I close the application and reopen it then TA_IsGenuineEx returns TA_FAIL and the application does not start."
With X & Y both being set to 1 day (not recommended!!), then yes, then next time the user starts your app after not being able to contact the servers it will return TA_FAIL.
See the documentation and example for how to prompt the user to reverify.
>> "a) can I keep the current values in GENUINE_OPTIONS and try to force TA_IsGenuine when TA_IsGenuineEx fails?"
Nope, see our examples for how to handle things. TA_IsGenuineEx() already contacts the servers. Just hammering the servers with another call to TA_IsGenuine() is not the solution.
Also, always use the latest version of TurboActivate. Currently that's TA 4.0.9.6.