I had a guy with 98 patience rating refuse to sign. It tricked me too. During the 3rd arb season, he said he would join a team that appreciates him more so I thought i lost him. Then, right after rollover, it showed that he was willing to re-sign. Then, once re-sign free agent cycle actually hit, he said he was going to free agency no matter what. So, if you intend to keep a guy past his third arb, I would NEVER take the chance that he would be willing to re-sign after getting ARB'd a third time.
I was getting mixed answers on this on the board, so I used trial and error and found out that I will never sign a guy to a third arb if I intended to sign him long term.