There are two ways I commonly break my cities:
Spending Money On Things Before Sims Want Them
Sims want things... schools, hospitals, parks... but they want some things more than others, and if you build them in the wrong order you are WASTING YOUR MONEY, because they don't have their full effect. On the quick reference guide, as well as buried deep in the Sim City Manual under the desirability chart, is possibly the most important information to the game that no one knows:
What (Sim City) Sims Want
Although you can’t directly affect the types of occupants that develop
in your city, you do have indirect control by affecting the desirability
of the zoned areas of your city. The following actions can be taken to
improve the desirability for each of these occupant types:
This chart is ORDERED. Residential Sims want police more than hospitals. Dirty/Manufacturing industry wants police, then shorter fright trips, then NOTHING else, they're happy. After you've taken care of the basics that every zone wants, power and water for higher density/$$$, take care of problems in this order and you'll spend less money, attract more Sims, and make more money. I'll repeat once more:
I think this is the most important info people are missing to building a great city.
Not Replacing Dying Utilites
The utilities buildings, water pumps, power plants, and incinerators age over time, more for the more they are used. They gradually cost more to maintain and have lower output. Eventually, you are paying out the nose for nothing. Replace them as soon as you can.
Special note, if you are using Waste To Energy incinerators, turn them down to producing no power and have them only dispose of waste. This prevents the plant from aging in any noticeable amount, and you can then buy your power from a cheaper plant. The downside is that your power budget will not be at 100%, so 1) new plants will start at whatever the budget is set to overall, and 2) there is a chance of fire on all power lines. So just don't use any... use low density commercial zone instead. Same power spread, no cost, possible income.
Best Answer
If your taxes are "near" maximum, then you're running with taxes in the 18-20% region, which will not only dramatically reduce demand for R$-R$$$ but also have a knock on effect in that your current population will also begin leaving, resulting in less available potential workers for both commercial and industrial buildings.
At a guess - since you've stated that you have your taxes at maximum as a method of making money - did you build your entire city infrastructure before allowing people to move in or something? Essentially, if you're at the point where you've built hospitals, schools, police and fire, but are not making a profit, then you're probably trying to expand quicker than your population is increasing, resulting in far more monthly expenditure than your income.
To increase residential demand, ensure that your residential zones are some distance away from buildings which are a source of pollution - power plants, industrial zones, etc - that you have a good road network between your residential, commercial and industrial zones to keep the commute time down, and reduce your taxes for the residential zone type you wish to create demand for. You can raise your taxes right from the start of the game from the starting 9% to around 11-12% but going any higher than this without the luxuries of happy citizens, parks, stadiums, etc will simply result in your population moving out and your zone demands plummeting.