Why doesn't my ryobi one + string advance?

SOURCE: Ryobi string trimmer 32.1 what do mix gas and oil or just gas?

Ryobi trimmers I have had use a 32:1 oil mix. Just pick up a little bottle of Ryobi 2-cycle oil and read it to see that it will give a 32:1 mix in a gallon of gas. Pour it into a gallon of gas, and maybe a little fuel stabilizer too, shake it up and you should be good for the season.

SOURCE: ryobi weed trimmer

I have one of this trimmers. It is simple to replace the line. 
-First line up the arrows on the bottom of the spindle. 
-Then feed the line back in one of the holes in the side of the spindle (this is the same hole that the cutting string comes out of). 
-You will see the line come out of the bottom of the spindle. 
-Take that line a place it in the hole on the bottom of the spindle. 
-Leave about 9 feet of string hanging out of the weed eater (do the same with the other side). 
-Then turn the inside wheel (I can't remember if it is clock wise or counter clock-wise but it will only turn one way) most of the string is rolled into the spindle. 
-Cut the string of about 5 inches out of the weed eater. You're ready to cut!

SOURCE: Ryobi Electric string trimmer

TJ, I've had the same problem since yesterday and I found the solution (lots of googling - that's how I found your post BTW).
It turned out that the switch malfunction is a common problem.

The part number for the FA3-4 switch is:

ut41002a-36 ("switch assembly")

Available here (thru Amazon):
http://factorylawnandgarden.com/product/553902/B000PLVCX8/SWITCH_ASSEMBLY_UT41002A_36/

It's a Homelite part, which is identical to Ryobi.

Here is the manual showing it (part 6):
http://www.m-and-d.com/pdfs/ryobi_tool/RY41002.pdf

Here is the thread with the solution:
http://www.ryobitools.com/dc/dcboard.php?az=show_topic&forum=112&topic_id=597&mesg_id=597&page=3

HTH,
Adi

SOURCE: Replacing Drive Shaft for a Ryobi 725r

The lower flex shaft should cost around $40, unless you order it online and have to pay shipping. You should be able to get one from your local MTD dealer. (Ryobi is owned by MTD)

SOURCE: Want manual for RYOBI 31 cc 700r weed eater

Try this link:
http://lawnandgarden.manualsonline.com/manuals/mfg/ryobi/700r_1.html

Testimonial: "Thank you! Just what I needed."