During period of illness, Maxim's about to stop getting worse (6,3)
I believe the answer is:
bottom out
'to stop getting worse' is the definition.
I can't tell whether this definition defines the answer.
'during period of illness maxim's about' is the wordplay.
'during' is an insertion indicator.
'period of illness' becomes 'bout' (I can't explain this - if you can you should believe this answer much more).
'maxim' becomes 'motto' (I've seen this before).
'about' is a reversal indicator.
'motto' in reverse letter order is 'ottom'.
'bout' placed around 'ottom' is 'BOTTOM OUT'.
Can you help me to learn more?
(Other definitions for bottom out that I've seen before include "What one getting to moon must have" , "reach the lowest point" .)