Kind of a follow-up to this earlier question: How could formamide lakes form on an exoplanet?
Suppose the problem of how to get an initial quantity of formamide is solved, and microbial life has arisen. It nevertheless seems highly unlikely that ocean-forming quantities of formamide, or formamide rain, will naturally persist on any realistic planet. (The Limits of Organic Life in Planetary Systems even specifically calls out formamide life as being most likely in desert environments, with formamide occurring in small quantities.)
So, if formamide life is going to spread, it's going to need to manufacture its own biosolvent.
There cannot be lots of water around, because if there were, a) life would've just developed to use water instead of formamide in the first place, and b) formamide will be long-term unstable. So, the water + HCN synthesis path is out, except perhaps as a component of a larger metabolic process that temporarily produces water internally.
Other possible synthesis paths include:
CO + NH3 -> HCONH2
HCOOH (formic acid) + HCN -> HCONH2 + CO
HCOOH (formic acid) + NH3 -> HCONH2 + H2O
4 NH3 + 2 CO2 (not environmentally stable) -> 2 H2NCOONH4 (Ammonium carbamate, used in the production of pyrimidines) -> 2 HCONH2 + N2 + H2 + 2 H2O
There are probably more, and some of these end up potentially interacting with each other. But the biggest issue seems to come down to "how do you get both oxygen and hydrogen without ending up with a ton of water in the environment?"
So, what would a reasonable ecology look like, in terms of biologically-relevant environmental chemicals and producer and consumer metabolisms, that would let formamide-based organisms exist and produce their own endogenous formamide?