That's only possible if there has been a paradigm shift that the original poster has not identified. He's stated a few times that his company is operating on thin margins. I'm gonna give him the benefit of the doubt and assume he's running an efficient shop.
I don't believe that leaves room for a "low cost" competitor at the bottom. And, unless it's a commodity, it wouldn't matter anyway. People who do these kinds of acquisitions make a check list...the product that checks off the most items on the list, and brings in a reasonable bid vs. all of the other bidders, gets the contract. It's not like consumer markets.
I still suspect the OP is charging too little, if his product is good, because being the low cost provider in just about any market is not a good place to be. Margins are thin, customer satisfaction is low (think eMachines and Packard Bell vs. Apple and ThinkPad) and you can't make enough to push forward on the projects that'll help you grow and provide better services.
This is precisely the thinking that leads to getting disrupted by a different business model.
Please re-read my whole comment (and the one above it). I've explicitly discussed paradigm shifts that change the shape of the industry. A "different business model" is obviously one such type of shift. But given the description of the situation, I don't believe the OP is in such a moment in the history of his industry.
That could be the case, of course. So, you're right, we are just taking a different view of the provided data.
But, your problem is not a paradigm shift that alters the competitive landscape. Your problem is a competitor with unsustainable pricing. Don't play that game. It's foolish and you'll lose more customers than you win by playing it. You'll also dig yourself an early grave (figuratively, and possibly literally, if you take your business too seriously).
Ignore your foolish competitor. Build better products, charge the right price for them (you may still be too cheap), and keep working. The low-priced competitor will continue to lowball his bids, and will eventually get a reputation for under-serving and over-promising. In a year or two, you'll have a chance to re-bid the same customers you lose this year. And the customer won't be so interested in getting the product cheaply.