Had a similar issue and think I found the solution.

Try inserting the date as a field instead, it should work.
I don't have 2007, so I don't know where you'll find it in the menus, but in 2003, it's under Insert, Field
Field Name = Date
In the Date formats box simply type: MMMM 26, yyyy

If this doesn't update next month as desired.... then try setting up both pieces of the date that you want updated as separate fields. ie. the month as 1 field, the date as text in the document followed by the second field for just the year. The formats would simply be MMMM or yyyy respectively.

If this is in a header or footer, remember fields in headers and footers don't get updated quite as predictably. If you have the date anywhere in the body of your document, you are best served using a StyleRef field in the header or footer to pick it up rather than putting a field in the header/footer.

Good Luck.