Usual problem when e-spin with nano particles. It is difficult to avoid when doing for long duration.
Better, keep the syringe pump horizontal.. (polymer in horizontal position). When keeping polymer solution vertically, gravity force may act and particles may quickly deposit.
In horizontal position, try large needle diameter (But it affect diameter of the fiber).
You may try ultrasonication of your spinning solution to get a good dispersion, which will prevent the clogging.
As you can see in couple of my publications, you may also try simultaneous electrospinning and electrospraying. That is electrospinning of PVA and electrospraying of a well dispersion of MWCNT.