Sorry to hear that your husband is having a pay problem, but to answer your question, "Why can't they pay on time?" - in fact, the Army does 99.9% of the time.
And curious - what is his current training? (I assumed your question was about BCT or AIT until I noticed in your signature line that he graduated back in 2008).
You can you talk to? Since he is the Soldier, it is his responsibility to talk to his pay person in his Reserve unit. If that is the person giving you grief, he needs to go up the chain of command, from 1st SGT to CO. If that doesn't get this settled, he needs to then call this office -
Army Reserves, if your pay chain-of-command has not been able to resolve your pay problem, contact USARC:
USARCPAYINQUIRY@usar.army.mil1-877-462-7782