If your mother's hypothyroidism is due to the most common cause, Hashimoto's Thyroiditis, then it is possible that the TSH is increasing due to her thyroid glands being gradually destroyed by thyroid antibodies produced by her autoimmune system. Far more important than TSH is whether she is having hypo symptoms. If you look through this listing of typical hypo symptoms, which ones does she have?
http://endocrine-system.emedtv.com/hypothyroidism/hypothyroidism-symptoms-and-signs.html
Since you did not list the reference ranges for the T3 and T4 rests, I can only assume that they are close to the ranges I am familiar with, in which case both tests are in the low end of the range. This is an indicator of being under medicated and hypo. It would be far better in the future for her to be tested for Free T3 and Free T4, rather than Total T3 and T4. The Totals are somewhat outdated and not nearly as revealing as the tests for the Free T3 and Free T4.
A good thyroid doctor will treat a hypo patient clinically by testing and adjusting Free T3 and free T4 as necessary to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not test results. If you want to read more about clinical treatment, this is a good link.
http://hormonerestoration.com/files/ThyroidPMD.pdf