My brand new 5960 did the same thing back in April. I brought it back to my AD who "re-synched" it. Now, all dates changed perfectly from Tue 30 Jun to Wed 1 Jul.
If you're unable to have your AD help you "re-synch" the gears, then follow you owner's manual to the "T" on how to properly set it. When the watch is just past 06:00, using the exact sequence as described in the owner's manual, set the watch to Mon 27 Apr. Then manually advance it to Fri 1 May. If this doesn't work, you've got a problem. Have your AD send it back to Patek.
I own a 5036 whose date never worked properly even after it was properly synched. It's problems were nearly duplicate to your 5140. Back it went to Geneve for 16 weeks ... Patek fixed it.
I'm sorry to tell you, but in my experience, unless it's a synch issue, these issues don't "fix themselves."