I just took a quick look at their earnings, and as of 12/31/2019, UA had roughly $5B in liquid assets. Its operating expenses were roughly $10B in the last quarter. Of that $10B/quarter, I'd estimate about $3-4B/quarter would persist through a shutdown (e.g. exempt salaries, rent, debt payments). So if UA completely shut down operations they could last somewhere between 4-6 months before running out of cash.
Of course, unless things get significantly worse, they will still be able to operate on a reduced scale so it's not clear how long they would be able to stay afloat on a reduced schedule.