Hi R3dWolfie,
Unfortunately I cannot reproduce - having used Kagi on mobile through firefox (with the extension + ublock) for a long while now.
We are aware of an issue on (seemingly only) ios devices where cookies randomly get dropped - which could play into this somehow (but we have no clue what causes it at the moment and have a hard time reproducing it).
One workaround for the time being, perhaps, would be to set your session link (you can find it in the control centre) as your search url in the settings - which includes a token which will reauthenticate you each time you search if you for some reason get logged out like the above. (just add a &q=%s to it when setting it in the search url field)