You have to be in Argentina six months a year, for certain. It gets tricky when you're on a precaria. You have to renew that precaria every three months. To renew it, you have to be within the country (absolutely no exceptions) when it expires and is up for renewal. It seems you have set obligations that will make this process very difficult for you unless you're able to decide the dates of your work travel. There is no waiver for traveling abroad for work while you're seeking residency here in Argentina if it interferes with renewing that precaria. Once you have a decision and are actually granted a residency, you'll still have to be in the country six months total per year (temporary residency) to advance to permanent residency, but you can travel far more freely...you'll just need to be in-country when your residency is up for renewal once per year rather than every three months(apart from 6 months of the year).
I hope that's not confusing, how I've worded it. Obviously, it's easier if you're not traveling out of country a lot as they asses you for residency, as it may signify you're not serious about living here if you're life is set up to take you abroad more often. I don't know how they figure things out behind the scenes, but I know they like to see people actually setting up shop as much as possible locally. I know it's hard when you're on a precaria and have other obligations, but bureaucracy the world over often doesn't make much sense. I hope it all works out for you!
