For a while the pilot would stay lit until the unit heated water, and then go out.

I guess she has no heat and had landlord problems with them not wanting to fix the heating system.

Separate meters , separate heating and cooling systems from the start 

(A) A landlord who is a party to a rental agreement shall do all of the following:(1) Comply with the requirements of all applicable building, housing, health, and safety codes that materially affect health and safety;(2) Make all repairs and do whatever is reasonably necessary to put and keep the premises in a fit and habitable condition;(3) Keep all common areas of the premises in a safe and sanitary condition;(4) Maintain in good and safe working order and condition all electrical, plumbing, sanitary, heating, ventilating, and air conditioning fixtures and appliances, and elevators, supplied or required to be supplied by the landlord;(5) When the landlord is a party to any rental agreements that cover four or more dwelling units in the same structure, provide and maintain appropriate receptacles for the removal of ashes, garbage, rubbish, and other waste incidental to the occupancy of a dwelling unit, and arrange for their removal;(6) Supply running water, reasonable amounts of hot water, and reasonable heat at all times, except where the building that includes the dwelling unit is not required by law to be equipped for that purpose, or the dwelling unit is so constructed that heat or hot water is generated by an installation within the exclusive control of the tenant and supplied by a direct public utility connection;(7) Not abuse the right of access conferred by division (B) of section 5321.05 of the Revised Code;(8) Except in the case of emergency or if it is impracticable to do so, give the tenant reasonable notice of the landlord's intent to enter and enter only at reasonable times.

You and your tenants may have an expensive surprize once the heat is turned back on. 

Bryce mentioned replacing the old shared heating with newer electric heating that was divided to the tenants.

Having lived overseas for a number of years I have grown accustomed to the mini-split heating and cooling used in many parts of the Middle East and Asia. 

.- Cap Ex, Maintenance, Vacancy should be 8+% for a 4-unit- Figure out the utilities situation (what you are responsible for vs. what the tenants pay)- Include professional PM (typically between 8-12% depending on your area)- The rehab required for the units and common areas- The electric/plumbing/heating (how old, last time maintenance or repaired, etc.)Best of luck!

Further, recent advancements in insolation, heating systems, and window materials have greatly improved the energy efficiency of new homes compared to homes built 15 or more years ago.

have you considered a heat pump system with backup electric heat?