Microtubule depolymerising drugs (e.g. nocodazole) block cells at the beginning of M phase, in prophase/prometaphase to be exact, because they prevent the assembly of the mitotic spindle. Inhibitors of CDK1 activity can be used to arrest cells at the G2/M transition.

As commented by Dr. D'Avino compounds targeting microtubules halt cell cyle at the beginning of M phase. While performing cell cycle analysis of compounds using FACS usually G2 and M phases are inseparable. Thus it is said that microtubule stabilizers and destabilizers arrest cell cycle in G2/M phase.

Further, as described above compounds interfering with microtubule dynamics are usually cytotoxic in nature. However microtubules are also reported to play a role in axonal transport, dysfunctioning of which may lead to neurodegenerative diseases such as Alzheimer's and Parkinson's. I suggest you to consider this aspect also. Here is a reference describing the effect on nervous system due to microtubule targeting agents. 

Brain. 2013,136, 10, 2937-2951.

There are various potential explanations for the lack of cytostatic effects, for example, your compound may bind microtubules but not actually inhibit their function, it may not enter cells, it may require higher concentration to show effects, etc.

So to answer your question properly it would be useful to know how your compound affects microtubules and how this was assayed. Does it bind tubulin or microtubules? Apart from binding, does it also affect polymerization/stability? Was this assayed in vitro or in vivo?