Alchemy Sphere items expire:
Because formulae are more unstable than standard alchemical items, they expire and no longer work after 24 hours
Tech is currently being overhauled, but as it is now as long as you retain the ability to have gadgets you can keep any you have even if you can not currently make that many (so long as you previously could in a day). See the rules:
you cannot prepare more devices at one time than a number equal to 1/2 your ranks in Craft (mechanical) (minimum 1) + the number of (gadget) talents you possess.
If you attempt to craft a gadget that would push your total beyond this limit, you must disassemble gadgets for parts until the gadget total is low enough to permit the new created gadget.
Gadgets require near constant maintenance from the creator
For the Trap sphere:
This trap persists for 1 round per point that your check exceed the placement DC.
They are simply a duration. There is no apparently limit on the number, but at some point your older ones will start expiring.
With Persistent Trap and Customized Weapon alters the duration, it is technically an instantaneous effect so losing that talent shouldn't affect placed traps. However the loss of skill ranks can impact the limit of Persistent Traps.