I have read through the rules reference several times and there doesn't seem to be an answer to this question.

If your upgraded trooper in a unit ends up being the last trooper in a unit, that trooper then become the unit leader and is replaced with the unit leader mini. Does this mean you lose the upgraded troopers weapon ability?

Here is a scenario; you have a unit of 3 troopers, 2 standard troopers with no cover and 1 DLT-19 Stormtrooper fully obscured by terrain. The unit is attacked and the only remaining trooper is the DLT-19 that is concealed by cover. That trooper must now be replaced with the unit leader mini. Does he still have the ability of the DLT-19 weapon?

No, the Leader mini cannot use the Heavy Weapon if he is the only model left, per the bullet under Weapons on pg.46 of the RRG:

Quote

While attacking, only the specific mini sculpted with this
weapon can use it, though it may choose to use one of
the unit’s other weapons instead.