Which flat roofing system requires the least maintenance?
I am not an expert in this type of roofing, I do however have some questions and recommendations that may help you get the right answers.  

First the questions.  Is this roof drained with an internal system or scuppers along the edges? How large (square footage) is this roof?  What part of the country are you in? Have you consulted an industrial/commercial roofing specialist?

Here in the north country, most flat roofs on larger buildings are treated in a bonded/welded rubber, neoprene membrane. All the edges, sidewalls, plumbing vents, chimneys etc must be properly flashed and sealed with bitchethane and bonded to the flat covering. It is also very important to know that a flat roof is actually not perfectly flat. They must have some designed pitch to a drain point/s. Any area that allows standing water is potential source for leaks. Proper drainage is essential and will prevent the majority of future leaks.

Since access to the roof seems to be an issue for you and the contractors you have consulted so far, consider the following:

Only deal with a contractor that owns or regularly uses a bucket truck or man-lift and is used to working on taller buildings, and has the proper safety equipment and trained personnel to safely handle the job and materials.  

Look at options to install a dog house access  on the roof. If there is no common area where one can be installed, explore the possibilities of an external attached caged ladder. Some method of easy access will allow safe, quick inspection of the roof.

Solving your problem should be fairly evident to a competent industrial/commercial roofing contractor. You may not like the answers you get, or the costs to fix the situation, but if you do it right this time, you will save money in the long run, minimize potential interior damage, and protect the value of your property.    Good luck.