Two regulatory reasons:
1. Holding the slot between the two terminals so no one else is able to have it. I'm assuming they've signed agreements with the terminals in question that they're going to fly X amounts of flights per X amount of time or they're going to lose the route. They're probably just making a bit of a profit with these routes and they're happy keeping it on. Plus they keep a presence in certain airports which is free advertising if done right.
2. Government forcing certain routes to stay open for some reason, or providing some sort of tax credit to companies to keep it open. I'm assuming this is done to ensure that rural areas are services properly. Or at least to have some sort of rural hub.
I didn't think there are too many flights in the air now though. Seems like airlines are cancelling a good deal of service. They may be told to keep paying people if they want federal money / stimulus money though.
to answer your questions
1. for decades now, there has always been a agency that pretty much 'auctions' off the slots under a yearly licence.
there is an international agency and also each country has domestic agencys.
its not about 'profit' its about if they stop flying for a month.. they lose the other 10 months of flying ability. so its just balancing the books of paying for ful for 0 passengers. and then knowing they can keep the slots for the other working year to make the money flying passengers then.. by not flying at all.. they would have been fined. and lost slots. so it would have cost them alot.
2. governments are not forcing routes to stay open or offering tax credits.. the airlines asked the agencies that in the event of a pandemic they can just stop flying without any penalty or slot licence loss.
3. governements didnt force them to keep flying. it was the airlines in january/february that thought that the cost of not flying was more than flying empty... but now that the flight coordination agencies agreed there will be no penalty. the planes ont have to fly purely to keep the slots.
....
as a separate thing. some airports are allowing flights. and airlines end up charging passenger stupid ticket prices. and as a separage thing. governments are 'hiring' commercial planes to 'repatriate' vacationers.
but airlines are not getting tax credits just for empty 'ghost' flights