An adhesive melter and a method for operating the melter enables predictive maintenance of an exhaust air filter used to remove pressurized air flow that delivers solid adhesive particulate from a fill system into the melter. To this end, the fill system repeatedly actuates to refill a receiving space, and a controller monitors a duration of each fill system cycle. When changes in a calculated average duration of a plurality of fill system cycles exceed a maintenance threshold, an alert is emitted at a user interface to prompt maintenance or replacement of the exhaust air filter before a complete shutdown of the fill system is caused by clogging of the exhaust air filter. Consequently, unplanned downtimes caused by clogged exhaust air filters in the adhesive melter can be minimized, regardless of any variable conditions occurring at the melter.