It's never really explained where the shortfall is, so we can only speculate based on what we more broadly know about the Mandrills. Do they lack sufficient trained techs? Do they lack sufficient parts?
To me that reference is an example of what we are told in canon. That the Fire Mandrills economy is rather small and inefficient. That the Kindraa setup causes a lot of duplication of caste roles between them. That the Clan as a whole tends to be on the resource poor side of the spectrum. And that a lot of the Clan's resources get tied up (and expended) through the day-to-day fighting with other Kindraa. This is often referenced in the fact that the lower castes don't have time for innovation, as they are tied up in the day-to-day needs of the Kindraa.
That kind of thing may be a lot more common among the Mandrills than we realize. It's very telling to me that everything says the Mandrills went into the Trials to decide which Clan would join the invasion, with a lot of battle damage not fully repaired.
Those Trials were the focus of the Homeworlds when they happened. Watched very closely everywhere. It was like the real world Olympics. Big event on full display.
Now imagine the opening ceremonies of the Olympics and the games of the Olympics and every nation is sporting shiny uniforms, shiny good-looking equipment, but one. That one team, their stuff looks a little ragged. The swim team's caps have holes in them that have been patched (instead of replacing the cap). Athletes for running events are wearing shoes that look like they are pretty worn out. The athletes from that team go to get their javelins for the javelin throw and some of them are cracked and have been wrapped or repaired instead of replaced.
That is the Mandrills.
By whatever name...burn rate, expenditure rate, I bet the Mandrills go through equipment pretty fast. Even if it isn't destroyed, it requires a lot of repairs and maintenance and the Mandrill logistical capacity for that is limited. The Mick-Kreese reference to a lot of airframes being down for maintenance is just one reference, to what I suspect is a much more widespread phenomenon among the Mandrills, especially during times of heightened frequency of Trials.
I think it's very telling that in Mechwarrior's Guide to the Clans, in the Fire Mandrill Kindraa Clash Tour of Duty, one of the possible roll results (6) reads that your (the character's) combat style is hard on the equipment. You spend most of the year dispossessed.
You don't see Dispossessed on many (maybe none, I haven't seen it) on the other Tour of Duty roll options associated with the Clans. That logistical reserve is prettys hallow.
In that same Kindraa Clash Tour of Duty a 5 roll results in: The pace! The constant fighting day after day....another alert. When does it end?
Yet a third roll reads "You should rest up more between battles" which sees an increase in military skills but a decrease in BOD.
That speaks to another aspect of the Mandrills. They don't have sufficient reserves to rotate units away from combat for long. Of course that takes a toll on the equipment, as well as the warriors, and the techs, everybody.
But if you truly were trying to solve this problem, the fastest solution is to win more resources (specialized techs, manufacturing facilities like an ASF factory or factories that produce component parts that go into ASFs). In general, you'd try to deepen the logistical resource. Shift or increase production of spare parts for example. If it's a manpower shortfall then grabbing some more ASF techs.
My gut feeling is that their logistical reserve capacity (spare airframe availability, spare parts availability, manpower/man hours) just isn't adequate. That they are forced to make-do with the bare minimum and sometimes less than that at times of Trial peak intensity. I also suspect that supporting 2 warships ties up a lot of their resources, particularly the Potemkin, that is a very big warship. Setting aside the fact that it's a Dropship carrier above all, in terms of resources required to maintain it, it's up there with the battleships.