I have the same thoughts as NeverarGreat. To me the relationship seemed warmer, in comparison to ESB. So it seems to me there was some more training or time together between the movies. Like in ESB, Luke said he would complete his training, so his line still works.

It may seem slightly off when Luke sees Yoda and he talks about being old … but added sick. When Lukes goes off to save Han, during that time Yoda got sick. The time span could be weeks from when he left Degobah to help save Han. So that whole scene still can work. An older person can get sick and go relatively quickly, even if you saw them weeks before. (happened to me a few times)