jasperd,
Depending on where you are, you don't need a bachelor's degree to be a technical writer ... but it really helps. It sounds like with your background in RFQs and contracts, that maybe you might want to look for positions that are hybrid technical writing/proposal writing (but be careful here - sometimes these types of positions require lots of overtime) or a junior technical writer or editor position.
Take time to create some samples. You can pick an open source project that needs help and write some documentation for them. Or, write up some technical tutorials and post them on eHow. That will help you with the portfolio. If you can incorporate video or screenshots/screengrabs - it can help you.
If you want to break into the field, visit the techwr-l website (
http://www.techwr-l.com/techwhirl/index.php3). When I was a technical writer, I subscribed to the list and learned a lot from them. You might also find other newbies.
If the doors keep getting slammed in your face, consider getting a certificate or starting to work on a degree. Even before you are finished, just telling an employer that you are working on a degree during your own spare time, can work wonders.
While it is a tough economy, switching careers it isn't impossible. Just keep learning and writing. If you have the money, consider joining STC (the Society for Technical Communicators) in your area - or at least see if they'll allow you to attend a meeting to investigate ... free of charge. You'll meet other technical writers there.
Keep trying and don't give up! Post here when you get your first gig. And, if you have specific technical writing questions, feel free to pm me.