My wife's work requires her to clock on and off using a program on her computer at work. Many times the program won't let her clock on in the mornings and she has send an email to her manager if she can't clock on so her time can be adjusted. They are now saying that they will no longer adjust her time, but it can be 1 to 2 hours before a manger arrives to help her clock on. Isn't it the responsibility of the empolyer to provide a working and accurate time clock for their employee's [if they require them to clock in and out]?

She is a non-exempt employee.

Well, it's not mandatory by law, per se, but in reality, it is, if they plan on using it for purposes of determining pay, at least.
Is she remotely based? Or can she manually record her time and have her supervisor/manager acknowledge that at the time it occurs?

In any case, assuming she is a nonexempt employee, she must be paid for all hours worked, period. I would recommend she keep her own record of hours, just in case she has to file a claim for unpaid wages with the state Dept. of Labor, if the company insists on not paying her for time she worked.