I think you should change the way that you use the term "continues" in the sentence. Both sentences depict an ongoing action, regardless of an interruption. However, being tired is not an interruption. It is a sense or a feeling of physical fatigue. You should be looking as to whether you want to present the action as ongoing (active voice) or past (passive voice). I would rather have you choose between these two presentations, depending upon what the paragraph is trying to depict:
- He continued to watch TV despite... (past tense, passive voice) - He continues to watch TV despite... (present tense; active voice)
Decide upon which time frame to want to use the sentence in, then choose the correct time reference for "continue" to create your sentence.