It might be a) the result of some cognitive bias, i.e. not quite true, or b) the result of your feeling undervalued and underpaid, which in turn makes you more likely to perceive what is actually an usual amount of problems as unusually annoying, or c) true, which raises the question, why?
With Virtualmin, we started out charging 50% the price we knew (and everybody else also knew; it was listed as being "on sale") we would eventually charge. I did find that the number of customers demanding even lower prices dropped to almost nothing when the 50% off discount ended. Those customers simply weren't in our market segment, and went back to second-tier products that cost dramatically less and offer dramatically less capability. And, I suspect, but don't know for sure, that cPanel and Plesk customers became more likely to migrate to Virtualmin after the price increase. But, I believe that has more to do with perception of value in an existing market with existing price expectations, rather than any particular price point.
Anyway, I believe the rule of thumb is roughly true. Cheaper products certainly attract a buyer that has weaker loyalties (as soon as they find a better price, they're gone). They probably are also more demanding.
We have a range of prices from $138 to $998, and I would wager that the $138 buyers are at least twice as likely to ask for support as the $998 buyers. I don't know how to make that more fair for us or the $998 buyer, however, since the pricing is based on usage, and a natural result of using the product more is being more familiar.
The point of all this rambling is that I don't think there are any hard and fast rules, but I do think charging more is worth an experiment for most companies. You can always revert your prices (and refund the "suckers" who bought at the higher prices) if things go badly. At worst, you'll learn that lower prices were a better position for you.
Paraphrased: if price is your selling point, you're likely to attract customers who care only about price and tell you they want it even cheaper or they'll go somewhere else.
The infamous race to the bottom, which is a place where very few companies thrive.
This is also a well known phenomenon in the web hosting industry.
My on-the-side consultancy initially was charging silly low rates to get some custom. It kinda worked but we ended up with demanding customers looking for a good deal at a low rate.
Now we feel established enough to raise rates the customers are a LOT better and the sites are rolling out a lot more smoothly all round!
My guess is that companies that pay more for software also tend to hire people to manage and provide tier-1 support for the applications they use. They also tend to take more time making purchases and thus better understand the capabilities and limitations of the software.
That's not to say that large customers (or customers that have paid more money) can't be demanding, but they're usually more understanding and less likely to be unreasonable when they contact us, and have more reasonable expectations around resolution times.
Also low income is correlated with low education/working class demographics, which have associations with being more demanding, rude, etc.
Your situation sounds like consulting/contract work so this is probably quite painful. But it's the right segment to target for mass market and volume products...