In general, there will be no explicit advance warning that your favorite place is about to close. There are however, some warning signs you can watch for:
The Hours Change
This is a big one. If the place was formerly open on Sunday, but now isn't, if they used to do lunch and supper but now do only lunch, if they used to be open until 10pm, but now close at 8, these are all bad signs.
They are Out of Something Mundane
If you go and they are out of something completely mundane and off the wall, like napkins, or salt, that is a very bad sign.
The Staffing Level Drops
If your favorite waitress is gone, and she has not been replaced, that is a bad sign. If there was a hostess and now there is not, that is a bad sign.
The Owner is Waiting Tables
If the owner just used to circulate occasionally checking to see that everything was OK, but then starts meeting you at the door, seating you and taking your order, that is a very bad sign.
They Drop the Sanitation Service for the Restrooms
If the restroom used to be Sanitized by Swisher, but now has a grocery store bottle of liquid soap, that is a bad sign. It's not that it isn't clean, it still is, but you know they can no longer pay to have it cleaned.
The Menu Changes
If the items that take more work to prepare, or which fewer people order vanish from the menu, that is another bad sign.
If your favorite place starts to exhibit one or more of these signs, well, enjoy it while you can.