It can and sometimes does happen.
The problem is caused by the plumber or installer cutting the plastic push rods to short.
The rod is supposed to be a push fit and locate into the button on the under side and hold the button securely into the hole on top of the cistern.
If it is not holding the button in place its been cut shorter than it should be. Try and place the button correctly over the plastic rod and push it down ensuring a tight fixing. If this fails contact the installer. It wont be long before you are on hear again asking us where you can purchase a push button for your particulat cistern....Very soon if you have children...
Pat
December 2008