Is there a certain amount of time until an item is considered abandoned, especially if it's a securable item?

There is no time but this should help.

AR 710–2
When property is found on an installation and when items are discovered in a unit and are not on accountable records (hereafter referred to as “found on installation”), the property will be turned in immediately. Found on installation property will not be picked up on organization property records. It will be turned in to the SSA in “as-is” condition. Units will not spend resources to upgrade found on installation property before turn-in. A document number will not be assigned by the unit. SSA will assign a voucher number to the turn-in after receipt. At ARNG units, found on installation property will be reported to the USPFO by using turn-in documentation. A document number will be assigned to the turn-in by the finding organization. The USPFO will direct movement of the property. Also, CCI that is discovered and is not on an accountable record requires the submission of an incident report per DA Pam 25–380–2.

Is this in regards to a FLIPL? All efforts will be made to find/re-secure the securable item until such time as Big Army deems it lost. As for the time, that will depend on how long it takes for that FLIPL to process.

Did you....or someone else....lose something that should not have been lost?

What do you mean? What's the context?