Is the original sentence ("Because of his illness, he lost opportunities to find jobs that might have been available to him") THAT incorrect? Why is it incorrect at all?
1. I agree that 'due to' is better than 'because', but the latter is not wrong.
2. You lose something only when you have had it. You miss something which is available but you not take advantage of. So, 'missed' or 'missed out on' are more appropriate.
3. When you talk about job opportunities, your 'might have been available to him' is redundant.
How about this: He lost opportunities to find jobs that (otherwise) might have been available to him owing to his illness. :?:
Doesn't "due" function as an adjective? Thus "due to his illness" is an adjectival (prepositional) phrase. That said, it could only be correct in a sentence like this: "his problem in finding job was due to his illness". Or am I wrong?
This sentence has a different meaning from the first.
:-?