Hi Bryan,
I am not sure about the 'more sensitive bone marrow' but some patients are more or less sensitive to TKIs. TKis in general can cause low blood cell counts and if this happens it is usual to stop therapy until the counts recover. Of course this depends on how low the cell count goes and for how long. In the case of low platelets, most expert clinician would not advise stopping therapy unless the count goes below 50. It is possible to support platelets with infusions, but in most cases stopping therapy for a while allows the marrow to recover.
Are you worried in general about this possible side effect or are you experiencing low cell counts?
Sandy