If you were pulling directly from the battery, 20 hours at 5 amps could be reasonable. The problem is that you aren't pulling from the battery directly, instead your UPS has electronics to convert DC to AC, and then your communication system probably has electronics to convert your AC back to DC.
You can roughly assume about a 50% efficiency when operating in this manor. With that assumption, lets look a bit about the power you are using.
Lets first convert to Watts as this will be the universal unit that can be used across voltages. 5 Amps at 12v is 60 Watts. I don't know anything about your communication system, but I will assume it could be pulling 60 Watts. If you take into effect the 50% efficiency, you will be pulling 120 Watts from the battery. It is a little hard for me to see the graph, but it looks like this will almost cut your life in half to about 11ish hours.
So 11ish hours is what you should be expecting at 25*C, but you are at -5*C, to make things easy I will assume it is actually at 0*C when you account for some electronics around it keeping it a little warmer. At this temperature you should be getting 85% efficiency, which brings your life down to 9.35 hours.
This is still more then the "less than 9 hours" that you are seeing, but I have also only roughly given some values. So I would say what you are seeing real world is within tolerance of my rough calculations meaning that there is nothing wrong with your UPS.
As a side note, I usually see people place backup generators in places that they might expect power outages for extended periods of time. The battery backup is there to pickup for the brief period before the backup generator kicks on and then also handles the transition back to grid power. Also many systems implement a battery backup that accesses the battery directly as to not have the DC->AC->DC conversion. I have seen this in security systems among many other places.
For sealed lead acid batteries, there will be some minimum level of ventilation required; they can give off hydrogen gas which is not poisonous but mustn't be allowed to collect in an unventilated space. Not a huge problem; just ventilate it as well as you would a bathroom.
For older (maintainable) batteries - does anyone still make them? there are some precautions to be taken during battery maintenance, against acid splashes.
And of course, never carry aluminium ladders in a battery room! More realistically in your installation, all battery terminals and high current circuitry should be covered and inaccessible to anything metal except when being worked on. (Accidental short circuits can melt screwdrivers and, in a proper battery room, ladders.)
I think that's about it.
Best Answer
Too small
Your inverter and your UPS are too "small". You have too much electrical load attached for the power ratings of those devices.
Why is there a UPS in there? A UPS (to the first-order) is just a battery + an inverter... which you, obviously, already have in your system.
Too inefficient
Also this is NUTS inefficient...
Approximately:
Battery (DC) --> Inverter (AC) --> UPS (DC) --> Devices (AC) --> Device Internals (DC)
You are converting DC and AC at least 3 times. Each time you lose about 20% of the power. So you are wasting half of the battery energy (e.g. it is running half as long as it could).
Follow-up
Monitor the voltage of the batteries and "hook a generator" when the voltage drops below 80% of nominal.
You can use a $20 multimeter for this and just check it every half-hour or so. There are also off-the-shelf devices for this.
That will be much cheaper, simpler, and more efficient. It will also improve battery runtime, produce much cleaner power, and continue to operate during the transition.
The tiny battery in the UPS will likely not be able to provide the instantaneous power to keep things running since it is much smaller than the larger batteries you use for primary power.
uh... ground it! ;-) Connect the center pin of the UPS's power cord to a copper pipe at least a meter long and bury the copper pipe in the ground (vertically if possible -- e.g. so it's at least a meter deep).
This will only work if you also have a ground-post (connection point marked "ground" or with the Earth Ground symbol) on your inverter that you connect to the same pipe.
If your inverter doesn't, I agree with @Johnny when he says:
You can buy copper electrical conduit pipe from a home improvement store for a few dollars.
I should also point out, that the goal here is simply to get the ground-fault light to turn off (by grounding the network). My suggestion should in no-way be considered a lightning protection system. Nor does it make use of anything that would give you ground-fault protection. Further, it probably doesn't meet the US National Electrical Code (NEC), which calls for a maximum 25 Ohms (DC) to ground. Typically, more than twice my recommended length is used to insure compliance.