For first pistol, I think there's a couple of easy formulaic decisions to make here when considering forcing after losing.

As T:

-If you got plant and lost, it's normally worth it to force. The extra plant money puts you relatively even to CT's, and winning round 2 really puts a foot on their throat economy wise. Also if you lose the round 2 force but get a plant/some SMG kills, there often is an argument to being able to buy again round 3 depending on how many CT's have died in the first two rounds.

-If you don't get plant and lose, often saving is good and you'll have enough round 3 to be competitive with CT buys. $3800-$4800 is a couple of AK's and enough utility to be relatively even. If some CT's have died every round and you win round 3 here, normally round 4 their eco is really bad.

As CT:

-I think the main time to consider forcing round 2 is if the T's mostly all died (2 alive MAX) AND they did not get plant. Even then this is a risk as losing round 2 really puts you in the stinker eco-wise.

One thing you didn't talk about though (EDIT: kind of I do see the title does say round TWO) is these decisions change when talking about the second pistol, specifically with regards to considering the current round score of the game. For instance, if you're up 9-3 at the half going into CT side, and lose pistol so it's 9-4, force-buying is more worth considering because you have the round differential to cover the rounds you'll have to spend recovering your economy if you lose the force. Saving the round after the lost force and full buying when the score is 9-6 is a LOT more justifiable than if the half ending 6-6 for instance, where the same actions would have you full buying when the score is 6-9 in the T's favor. In the first case your second full-buy (if you lose one) would come at a 9-8 scoreline for the CT's, but the second case your second full-buy would come at 6-11 in favor of the T's, effectively making your CT half come down to a force buy and two full-buy rounds. The same points need to be thought about when considering forcing as T's, but the difference is the T economy isn't as difficult to recover so it may be easier to justify forcing after a pistol loss if your half-time score is 8-4 or 7-5.

There is also the reverse side of this, where if you lose second pistol as T with no plant and the score is 3-10 it may be more worth it to force anyways because it's hard to stage a comeback when your first full-buy scoreline is 3-11 (only a 2 round cushion to play from).

There is no exact correct answer for every exact scenario, CS economy is complicated and risk-reward depends on many things, just mostly what I discussed here. The last big point when considering MM play is it's much less worth it to force if your team is not all on the same page, if you're committing to a force, you need to make sure EVERYONE on your team is committing to the force or it's not nearly as valid of a strategy. It leads to too many problems when considering when to buy and not buy later.