Unfortunately yes. There is a subgroup of HPV positive patients that do not respond well to chemo and radiation. As yet, they do not test for this.
My Husbands BOT tumour was fund again, 10 months post rads and chemo.
He went on to have salvage surgery of total Glossectomy and Total Laryngectomy. That was in March 2012. He is alive and well.
Tammy

Caregiver/advocate to Husband Kris age 59@ diagnosis
DX Dec '10 SCC BOT T4aN2bM0 HPV+ve.Cisplatin x3 35 IMRT.
PET 6/11 clear.
R) level 2-4 neck dissection 8/1/11 to remove residual node - necrotic with NED
Feb '12 Ca back.. 3/8/12 total glossectomy/laryngectomy/bilat neck dissection/partial pharyngectomy etc. clear margins. All nodes negative for disease. PEG in.
March 2017 - 5 years disease free. Woohoo!