I've no experience with chlorinated latex (but am interested in investigating it further) but I would suggest that if you have left latex out for some time it may have degraded due to UV light.
Generally it is advised that latex is stored in a dark place to avoid any UV impact on it. I don't know how long it would take to degrade but presumably it would also depend on the intensity of the light coming in. Here in the UK it may not be such an issue 😜
I also don't know if chlorination would make it more/less likely to be susceptible to degradation, either by UV or some other means.
Other things which can degrade latex is salt from sweat and any form of oil. You need to make sure that after using your latex items that you clean them with soapy water and rinse them well, allowing them to dry before storage. A dusting of cornflour is good to prevent them sticking together. If you latex items are left out in your room there's a chance they could come into contact with other volatiles in the air. Over time even spraying deodorant or hairspray or the like nearby could potentially lead to some degradation.
Some metal items are also known to discolour latex if they come into contact, but I'm not aware this leads to actual degradation though.
A good site for advice on storage and cleaning is this https://www.catalystlatex.com/cleaning-and-drying
Ultimately, ensure your items are cleaned using soap and water and well rinsed.
Dry the items well.
Store away from sunlight, probably in a closet or similar.
Look after your latex and it will look after you!