Strange.
Storing your database in program files is not a smart move, security wise (unless it's a read only db, I suppose). See the wiki articles on cross platform programming and windows for some ideas on where to store data files.
You might be having permission problems (access denied) - but then it's strange it works at design time and not at run time.
Edit: oh, if it works at design time, not at run time: please make sure the firebird embedded dlls are present in the application directory (or windows\system32 directory, I suppose, but I wouldn't go that route).
Hint: posting your Lazarus version, platform (obviously some form of Windows) and actual code is not a bad idea when posting...