The affix kha comes in the sense of 'what bears it' after the word ekadhurā being in Accusative -2nd case construction, the affix is optionally elided too.,
The elision is optional. Thus एकधुरां वहति = एकधुरीणः or एकधुरः ॥ The compounding is taddhitartha (एकां धुरं वहति) to which is added the samasanta अ, and then the affix ख ॥,