I know this is a common problem: the rank condition isn’t verified and solving it is mostly a matter of debugging.
After days of unsuccessful debugging, I am trying to find a strategy to figure out what could be the problem.

From previous posts I gather the following recommendations:
A) check the timing
B) focus on checking pre-determined variables
C) simplify the model and see if that helps
D) introduce lump-sum taxes so that the government budget constraint holds

Did I miss anything?

In my specific case, there are three things, throwing me off:

if the price stickiness (the Calvo parameter) is low enough, it works.

surprisingly: If the reaction of the nominal interest rate to inflation in the Taylor rule is weak enough, it works (this is surprising because usually, determinacy requires a lower bound on that parameter, yet I have to decrease it)

even though the rank condition isn’t verified, IRF’s can be generated and look reasonable.

I understand I am shooting in the dark here, but maybe someone has a good idea of what it could be (I am looking at a New Keynesian model with capital and two types of agents, only one of which can save (the savers are a small share of the population)).

You should try to find out if there is an economic mechanism causing the result. What happens if the share of savers is large? In that case, you should approximate the basic NK model and the standard Taylor principle should hold.

Also, I don’t understand how you are getting IRFs if the rank condition is not satisfied. The model should not solve in this case.

Thank you very much!
Indeed, sometimes it can’t generate the irfs, but sometimes it can (I was also surprised).
Increasing the share of savers is a good idea, I will try it, thank you.

One more thing I noticed:
If I close the government budget constraint with a lump-sum tax on savers, it doesn’t work.
However, if I close it by adjusting the tax on their labor income, it does!
I am happy this works, but very confused why.

thank you very much for your help!
I am not sure about the distinction.
The problem is that it says: “rank condition not verified” and that the number of eigenvalues with norm larger than 1 does not match the number of forward looking variables)
It can, however, compute the steady state.
stoch_simul then fails (not always but mostly).