Your employer is correct - IF your absence is for one of the very few (and rigidly controlled) reasons for which docking an exempt employee is permitted under the law. They are:
1.) If it is your first or last week of employment and you do not work the entire week
2.) If you are absent for one or more full days for personal reasons other than sickness or disability
3.) If you are absent for one or more full days for reason of illness or disability, on condition that your company has a bona fide sick time policy with a reasonable number of days and you either have used all the time available or are not yet eligible for it
4.) You are on FMLA (in this instance, and ONLY this instance, your pay can be docked on either a full day or partial day absence, whichever is applicable)
5.) As a penalty imposed in good faith for a major safety violation (and ONLY for a major safety violation - suspensions of less than one week for any other reason must be paid)
If your salary has been docked for any of these reasons, that is a legitimate, legal deduction, permitted under both the FLSA and the new Fair Pay Act, which does not in any way invalidate your exemption.
In every state it is also legal to dock a time bank (vacation, sick or personal time) for full day absences with or without the employee's permission, and in every state except California and Washington (where some restrictions apply) it is legal to dock a time bank in partial day absences as well.
If your pay has been docked for any reason other than the above, then you may well have a legitimate claim, for which you can file a complaint with the state DOL. It is doubtful, however, that one (or even a couple of) occurance(s) will serve to totally invalidate the exemption, (assuming that you are legitimately classified as exempt in the first place.)
Edited to make the following correction;
Under the Fair Pay Act, which goes into effect on August 23, the restriction that ONLY a suspension for a major safety violation can be docked is expanded to include ANY kind of disciplinary suspension, not only for a safety violation.