Hello,
I am using Sofistik2020 educational license for solving a nonlinear problem and I faced a convergence error in the following part of my analysis:
“
HEAD
SYST prob TH3 TOl -0.01 PLC #lf-1 ; grp 11 off ; ctrl iter 3 v2 1 ; ctrl beam 5
sto#iter 900
ulti #iter fak1 0.01 dfak 0.002 pro 0.005 fake -0.0001
LC 1001
LCC 902
END
“
I have to mention that I changed the progression of the load factor many times, but it did not help solve the convergence problem.

I checked other analyses as advised.
First of all, doing a linear analysis is not my interest because the problem is geometrically NL.
But I have changed the analysis to linear (see below), Although the results were incorrect, it did not show any convergence error.
" HEAD
SYST prob line TOl -0.01 PLC #lf-1 ; grp 11 off ; ctrl iter 3 v2 1 ; ctrl beam 5
sto#iter 900
ulti #iter fak1 0.01 dfak 0.02 pro 0.5 fake -0.0001
LC 1001
LCC 902
END"

I also checked the buckling eigenvalues, there was no convergence error but the results were much higher than expected. The first mode of buckling gave a load of 4kN, and the second mode gave 9kN as you can see in the attached image. But the nonlinear analysis gave the value of 1.86 kN (with the mode similar to the second buckling mode). You can find the graph below.
"+PROG ASE urs:6
HEAD
SYST PLC #lf-1 ; grp 12 off ; ctrl iter 3 v2 1 ; ctrl beam 5
EIGE 10 BUCK LC 902 LMIN auto
END "

I switched back again to the TH3 analysis, where I changed the pro and dfak as follows. at some steps, the model did not converge and then the convergence was achieved as I attached the print screens below.
"HEAD
sto#lf 15 ; SYST prob TH3 TOl -0.01 PLC #lf-1 ; grp 11 off ; ctrl iter 3 v2 1 ; ctrl beam 5
sto#iter 900
ulti #iter fak1 0.01 dfak 0.02 pro 0.5 fake -0.0001
LC 1001
LCC 902
END "

What I see is that you have a snap through problem like the Mises’ truss.
Go and check sofistik’s benchmark verification example no 31 - snap_through.dat for displcement controlled,loading. Program cannot converge in zone of snap through when load is load-controlled, but since your load step is small enough I see after snap it converges again.