It really depends on the pump technology and the reason for the minimum. I'm guessing (why am I guessing? because the OP didn't provide the information) that the pump is dynamic and that the minimum has to do with the actual pump fluid dynamics. This happens in a Jet Pump, where falling below the minimum power-fluid mass flow rate causes the pump to stop pumping altogether.
Another possibility is that the pump design uses process fluid to cool the pump and in that case BigInch's comment is right on, you've got a few minutes before heat build up damages something.
If you are talking about a centrifugal pump, you will find that operating at this flow rate will give greatly decreased life to bearings and seal(s), due to the shaft bending that will occur. In some cases, I have seen shaft failures due to repeated running at very low or 0 flow.
What needs to be known is what is the BEP of the pump, and how close to "shut-off" will the pump be running at the lower rates?
There are a lot of factors that need to be known before an answer can be supplied.
However, if you are installing a pump in a system that requires such variations in flow, I would look at installing a VFD, this is of course if you can operate it at lower heads as well.
Typically if the pump is running within the perameters of the pump curve, you are ok.
If you are running off the curve you are sure to experience problems.
