I suppose it depends on the kind you have.
The kind that fastens to the wall with clips and has a single leg:
Maybe. The whipping of the "not fastened" end could over time loosen the screws or enlarge the holes in the aluminum frame if left up. Having said that, many leave it up constantly and have never had a problem.
The kind with folding legs: The top is extremely heavy and the legs are extremely weak. The table has toppled onto the dinette seat several times (typically stopping quickly for a traffic light) and if you stored a fragile item on the seat it could be broken.
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW