Tempsford, whilst I'm not going to do anything as drastic as resign, I've had a very similar experience. After encouragement from several senior colleagues - and like you responsibility for a lot of aeroplanes and people (although not a budget for some years - we have other people for that) I made an application for Fellowship.
So I applied, and about 3 months later got a very bland letter from an administrator saying that I wasn't considered suitable. What really irritated me, was a blank refusal to explain the reasons why.
Having in the couple of years since won a couple of national engineering awards and finished my PhD, I shall have another go this year. If they turn me down, I probably won't resign - but I shall certainly go straight to the president and demand a clear explanation of the reasons why.
I do suspect that if you are not part of a major university, Big Airways, or the RAF the RAeS does tend to think that you are a minor player not worthy of fellowship - or in my case even an explanation of why! But, no I won't resign - I prefer to make my protests internally.
G
N.B. Just after I got my rejection for FRAeS, a junior of mine who had held his CEng for just under a year (I've had mine for nine) got the same "think about regrading to Fellow" letter as you did. You can guess just how I felt about that.