No convergence in iteration loop - Steady state simulation

I'm running a small test case to better understand how the results from FEFLOW using free and phreatic surfaces compare to an analytical solution using the Dupuit approximation. I'm interested in finding the hydraulic head between two drainage ditches with constant recharge at the ground surface, and I'm using a steady-state, phreatic model (attached).

When I run the model, I get the warning "No convergence in iteration loop at time: 1.000000e-03 with remaining error: 1.500743e+02 greater than  1.000000e-03."

I'm wondering:
1) In general, how do I know when warnings about convergence are something to be concerned about? Should I always expect model results to be unacceptable if I get a convergence warning?
2) Why is there a warning at "time:  1.000000e-03" if this is a steady-state model? (I wouldn't expect time to be a meaningful descriptor in this case.)
3) What changes could be made to this model (or a model in general) to fix the convergence problem?

Feel free to respond to any of these questions that you can help with. Many thanks!

[b]1) In general, how do I know when warnings about convergence are something to be concerned about? Should I always expect model results to be unacceptable if I get a convergence warning?[/b]
In principle I always would critically inspect the results with regard to numerical artefacts and I always would try to improve the model to reach convergent computational findings.

[b]2) Why is there a warning at "time:  1.000000e-03" if this is a steady-state model? (I wouldn't expect time to be a meaningful descriptor in this case.)[/b]
You are more than right. “Time” is not a meaningful descriptor. The word may be rather considered as a dummy-time, which has been introduced in times when FEFLOW was born. Since then the word “time” has been changed to a more descriptive word, because the difference between steady-state and transient is clear.

[b]3) What changes could be made to this model (or a model in general) to fix the convergence problem?[/b]
One option is to switch from steady-state to transient by keeping the boundary conditions and material properties constant. In this way you allow the system to evolve through time to reach a steady-state solution. Another option is to increase the residual water depth for unconfined layers in the Problem Settings. Please note that this option may introduce an artificial wetting of the “unsaturated zone” to archive numerical stable computations. Given the fact that the system is very dry, I suggest to solve the Richards equation instead of Darcy.

Thanks! The tip about increasing the residual water depth was helpful in this case. (On the other hand, switching over the the Richards' equation did not cause the model to converge.)

Sure. You need to define adequate parameters for the unsaturated flow modelling carried out by the Richards equation. This means you need an empirical model to relate saturation and negative pressure, saturation limits, etc. By the way, analogous to the residual water depth in the Phreatic approach, you will also need to setup an adequate residual saturation limit proper for the material properties.