Every response you received has been valuable and (IMO) right on the money economically (bad pun).
Realistically, you have a decade old economy instrument; therefore replacing the neck may be a realistic solution as a "beater" may be available at a very low cost.
IF you have given the neck time to adjust and no changes have been seen [I agree] that the rod may have been unseated. One of the reasons why the suggestion for 1/4 turns be made for neck adjustment is made by many manufacturers is the [relative] ease in which the rod may be damaged.
Using spacers (washers) might be productive. Remember to plan for any alterations in extra space for even very small washers. However I would take the neck off and very carefully see if you are getting any "bite" when the rod is turned CAREFULLY.
When you do this place your ear to the wood and LISTEN for a free spin. IF you hear the rod turning free within - you should plan on getting another neck, etc.
Here are some links to help you visualize.....
http://www.lmii.com/carttwo/Secondpr...s%2FNeck+Parts
Look at the Warmoth rod as an example or round "glue-in" rods:
http://www.warmoth.com/Guitar/necks/trussrods.as
Notice "square-end" rods:
http://www.alliedlutherie.com/truss_rods.htm
Here, if the wood does not provide firm purchase, the rod will unseat (spin). Some rods have "ears", some have square threaded joiners, some are round completely. Since the economy guitar influx, you may not know exactly what was used even with a "Fender Guide"; as the mfg of the neck would be independent from original specs & therefore can be broken [& repaired] in differing ways.