On top of that, the sewer lines started backing up, the tree fell and broke the fence, the wall started leaking, the hot water pressure malfunctioned after the water heater was replaced, and last but not least, we had a scorpion intrusion...

Can you reset a malfunctioning modulator/demodulator? 

Normally it is the responsibility of the tenant to report malfunctions or needed repairs to the landlord/property manager in a timely manner.    

Tenant agrees to allow Landlord timely access to premises to do maintenance and repair.Tenant will notify Landlord in a timely manner of any damages or problems as they arise, including damages caused by Tenant, malfunction of appliances or fixtures, and water/moisture leaks and spots.Tenant will take care of the premises, keeping them clean and clear of debris.

It will cost $13.19/month but is supposed to cover parts and labor whenever it malfunctions.

Tenant agrees to allow Landlord timely access to premises to do maintenance and repair.Tenant will notify Landlord in a timely manner of any damages or problems as they arise, including damages caused by Tenant, malfunction of appliances or fixtures, and water/moisture leaks and spots.Tenant will take care of the premises, keeping them clean and clear of debris.

The worse scenario is the heater could have malfunctioned over heated the water and ruptured. 

Tenant agrees to allow Landlord timely access to premises to do maintenance and repair.Tenant will notify Landlord in a timely manner of any damages or problems as they arise, including damages caused by Tenant, malfunction of appliances or fixtures, and water/moisture leaks and spots.Tenant will take care of the premises, keeping them clean and clear of debris.

This could be the result of undersized supply wiring or malfunctioning components in the furnace.

Here is an example from our property rules:APPLIANCES.Appliances included in the rental of the premises, as noted in the rental agreement, such as a refrigerator, range, dishwasher, clothes washer or clothes dryer, belong to Landlord.If Tenant wishes to use these appliances, Tenant agrees to use them properly in accordance with manufacturer instructions and assumes all responsibility for their care and cleaning.In the event there is a malfunction of an appliance or an appliance is in need of repair, Tenant agrees to notify Landlord in a timely manner and in writing.If Tenant wishes to use their own appliances, Tenant agrees to contact Landlord in advance to obtain prior written approval and instructions, as the removal and installation of appliances must be done with care to prevent damage to the appliance and/or building.Relying on text messages for official communications is not a good way to go.