If you are struggling or marginal and a sole proprietor you won't as for a start any sensible bank puts you in a higher risk category. This is an example of where Fran's recent content would make that all the harder.
But what if you had say a 50% deposit? Wouldn't that be a slam dunk for any sensible bank?
You would think so, wouldn't you?
The problem in the US is that a lot of banks are either extremely risk-averse or are large enough to not care.
If you have a perfect credit score, a "normal" easy-to-sell property, a large down payment, and a lot of wage (not self-employed) income, then things are fairly easy. The more ways you differ from this the fewer options you have.
One thing most people don't realize is that a very large percentage of loans (almost all?) are done through an automatic underwriting package which uses verifiable information to come up with an approve/deny based on weighted factors. There are still manual underwriters out there but they're few and far between. The automatic underwriters all seem to have 'hard qualification' issues.
For instance:
1) I've attempted to get a loan on a property which had a residence on just over 20 acres (like 20.05). A lot of lenders won't write on anything over 20 acres. Even if it was 20.05.
2) A lot of lenders won't write to anyone who doesn't have wage income (as opposed to self-employed income).
3) A lot of lenders won't write to anyone who has a business on the property. For example FHA (government guaranteed) loans don't permit loans on property with over 25% of the square footage being dedicated to business or non-residential use.
4) A lot of lenders won't write for anything slightly unique. I once owned and lived in an old church which had been converted to a residence. Because it looked like a church, most lenders wouldn't even consider a loan. Add in the fact that I've pretty much always been self-employed, and financing it and refinancing it was typically a year-long process due to repeated rejections from different lending companies, usually due to the nature of the property, even though there are several properties like this in the neighborhood and they have historically sold very quickly - assuming a buyer can find financing.
5) If you have a business on the property, many home insurance companies won't write an insurance policy. All lenders require you to have an insurance policy in place.
6) If you're self-employed, lenders are VERY VERY fussy about proving consistent income which meets their thresholds and rules. Anything perceived as not long-term is often a disqualification.
Combine more than one of the factors above (and probably others), and you'll find that getting loan is very difficult. Especially if you don't have a perfect credit score.
My experience has been that down payment actually makes little difference to the lenders. All they seem to care about is that you have either 20% to not have to pay extra for mortgage insurance, or if you qualify, even less is accepted but with mortgage insurance being charged every month.