"I became tired again."
Done! It may take a few hours before it's live at https://www.duolingo.com/skill/kl/Change/tips-and-notes .
Thanks for the suggestion!
If you have suggestions for improving the wording, feel free to tell us.
Furthermore, -qa' already contains the idea of start again. Another translation of -qa' is resume. jIDoy'qa' I resume being tired.
If you want the resumption of tiredness to take some time, i.e., I started to tire again, but I'm not gone getting tired, you can use the continuous suffix. jIDoy'qa'taH I continuously resume being tired.