The construction ‘try as * might,’ means that someone is trying very hard, but they still cannot do it.
In the English Grammar Profile, point 219 in the category of MODALITY is defined:
‘try as I might’ for emphasis at the beginning of a sentence.
An iWeb search for . Try as * _VM
1 . TRY AS I MIGHT 408
2 . TRY AS WE MIGHT 158
3 . TRY AS THEY MIGHT 154
4 . TRY AS YOU MIGHT 150
5 . TRY AS HE MIGHT 140
6 . TRY AS I MAY 55
7 . TRY AS SHE MIGHT 42
8 . TRY AS YOU MAY 31
9 . TRY AS WE MAY 28
10 . TRY AS THEY MAY 27
11 . TRY AS IT MIGHT 19
12 . TRY AS HE MAY 13
13 . TRY AS HE WOULD 11
Here are the best real-world examples that do not contain the limiting ‘I’ or ‘beginning of a sentence’. We still believe they all point to C2 proficiency. Especially, if you believe rarer examples of a stucture tend to indicate higher proficiency.
- Octavia‘s been after it for years but try as she might, the defenses thwart her. TED
- But try as he might to bend the forge to his will, its fires only produced other artifacts. TED
- The doctors, it seemed, never really had enough time for all the patients, try as they might. TED
- Try as he might, he couldn’t get away from her. TED