This is standard behavior for fields with global storage specified when you have opened the file as the client of a hosted database. Not only do the values not persist, but any change you make to a global field will not be seen by other users. This is generally a good thing as you don't want one client's modification of global fields to interfere with values entered by another.
See this knowledge base article: http://help.filemaker.com/app/answers/detail/a_id/3604/kw/global
I use graphic objects in layouts too, but I don't place them in a field, just make a file at the size I want and in layout mode, Insert Picture, navigate to where it is, and place it.
If made in a graphics program, make the canvas size (paste board, etc) the size of the outer dimensions, then when making the pdf (which works well), it will be that size.
Same considerations per normal for resolution, ie printing or display viewing.