depending on the type of non linear analysis you used, then conceptually the analysis takes the following steps (again depending on the type on analysis you use):
An iterative process starts:
- A small increment of the load $\Delta F$ is applied (typically a percentage between 1% and 10%)
- For those small load increments the displacements $\delta_i$ are calculated.
- on the resulting structure the loads are applied again and the displacement is calculated $\delta_{i+1}$
- The $\delta_{i }$ are compared to $\delta_{i+1}$. if $|\delta_{i+1}- \delta_{i}|\le \epsilon$ (where $\epsilon$ a small positive number), then you proceed to the next increment of the load.
Otherwise you return to step 2 setting $\delta_{i+1}$ as your initial displacement and your repeat the process . If the cycles repeat more than a predetermined number of iteration $n_{max}$ then the algorithm returns to step 1 reduce further the $\Delta F$.
What happens in a less stiff structure, is that the displacement will be (invariably) larger for the same load. As a result, step 4 where the check occurs will take longer to converge because at each step $|\delta_{i+1}- \delta_{i}|$ is more likely to be larger.
Additionally you might have more occurrences where you need to go back to step 1 and reduce the increment.
