Your problem is a) that takes several years of experience after graduation to become an engineer (as in all professions) and b) (as you've mentioned) most engineers work for large companies. Now, is a company going to invest in you if by the time you are ready to add value you are also looking to retire? It's not ageism - covert or otherwise - I work with many engineers who are somewhat older than you are now (in fact only last year I recruited an engineer, albeit an highly experienced one, in his mid-50s). It's more to do with returns on investment: if a company's going to spend 3-5 years training someone up they want to see a return.
(Incidentally, slightly off subject, this is why it's so hard for all recent engineering graduates to get jobs: most companies struggle with the concept of spending years training someone only to watch them immediately leave and work elsewhere. In my company we've found a solution to this, but it does involve being located in a really nice part of the country with no other jobs nearby!)
Okay, so that was the bad news, now try looking at this from a different angle, why engineering? If it's just because there's a skill shortage then that's probably the wrong reason. The skills shortage relates to the fact that there isn't a new generation of engineers coming through with modern experience; there are already hordes of us over 50s with aging engineering experience that no-one knows what to do with! BUT if it's because you're fascinated by engineering and can see a niche in which you could fit more-or-less self employed then go for it. You will (I'm guessing) have the experience of managing yourself, possibly of knowing how to make a business work, very probably of how to deal with customers and suppliers, and all at a much deeper level than a 22 year old graduate. However to make a start don't expect much (i.e. any) support from large companies, for the reasons above. It's far more likely to be the one-man-in-a-shed type operations that will give you a chance to get started, there are a surprisingly large number of these around nowadays who would be grateful for an extra (cheap and reliable!) pair of hands. Computer repairers, small design consultancies, musical instrument repairers, domestic appliance services, those sort of people are all worth approaching for a chat.
Regarding the volatility of engineering, what job isn't volatile? Civili service, teaching, banking, building, all these jobs have been considered safe at one time or another. My experience over an embarrassingly large number of years is that engineering is no worse and no better than anything else.
All personal opinions of course! You need to get a range of views on this, have a look on this site at your local IET branch and go along to some of their events (they should be open to non-members), hopefully the "coffee break chats" should help.
Andy Millar CEng MIET CMgr MCMIhttp://www.linkedin.com/in/millarandy
"The aim of argument, or of discussion, should not be victory, but progress." Joseph Joubert