As an FYI, yes Li-Ion batteries if left for a long time will get to a point where they no longer hold enough charge to operate. The same goes for rechargeable version.
Li-Ion batteries actually like to be punished to give their best life span and charge capability. Charging them frequently gives the best long term result for life span.
Unfortunately you don't have that luxury with the non rechargeable kind. There is no guarantee how old the battery is in your i-comm. it may already be years old when supplied to the maker of the i-comm device, so there is a very likely possibility it is already depleted as unfortunate as that may sound.
Of course you may also have a faulty i-comm device, this can't be discounted, but the battery is always the first port of call.
The i-comm battery does not run your system, the power of your AKER amp is the main power source. The battery within the i-comm unit maintains a consistent current and allows to functions to operate and holds the memory of your clicks and chirps.
1. are you using the mic that came with your AKER amp?
If not, that could also be part of your issue.
Microphones also play a lesser part in the potential problems with i-comm units.
2. Are you using an AKER amp? I believe these were originally recommended by the maker of the i-comm system.
3. moisture and the 3.5mm connectors can also play a role in the malfunctioning of i-comm units, so there is a lot to consider.
Generally I have found through experience of repairing i-comms for my garrison mates, there are numerous reasons why they fail.
Be mindful if using my work around that they are very fussy with the voltage from the power source so only use a 3.6 to 3.7 volt battery if you are going to attempt my mod.
I found with the rechargeable options, only purchase the batteries that have the overcharge protection chip in them and only use a digital charger that also monitors charge rates.
Other option is as has been mentioned, buy another battery same as is standard and try your luck.
Ultimately, I am sorry you are facing these issues with a new unit, have you contacted the maker to discuss, as I am sure they will also have several suggestions you could try.
Apologies for the wall of text but I would rather offer you as much info as I have, to assist you on finding a potential remedy so you can enjoy your trooping to its upmost