Electric fuel gauges are electromagnetic devices, with a
reference resistor inside them against which the sender's resistance is
measured. If that resistor is going bad, with its resistance decreasing
as it warms up, the gauge will sag.
However, except for an outright short, most resistors
increase in resistance when warm, so I would suspect a corroded
connection in the wiring of the gauge or in the line to the sender.
Look closely at the crimp connectors in the sender line at the gauge
and sender. Make sure the sender's body is properly grounded to the
airframe. There's also a connector where the wire passes from the
fuselage to the wing, and these get dirty and corroded and loose.
Perhaps a resistance measurement immediately after
disconnecting the wire from the gauge when the sag has occurred
(everything still warm) might reveal something. Full tank should be
around 30 ohms, empty about 150, IIRC.

Dan