Having worked the other side (i.e. having rostered crews for a really small start-up company as well as flying for it), i got a pretty good idea of how crew behavior changes with factors like workload, morale, etc... Fiona, you are certainly not alone in your behavior.
On the other hand, 3 to 4 days a month is an AWFUL lot to be sick, and in my day I would have caught and "corrected" that behavior inside of 3 to 4 month maximum...
An occasional sick-out can be justified, in my opinion, if you feel that the guys and gals at rostering do not take you seriously, or don't want to waste their time doing a proper schedule... I certainly know that happens... But if it's a regular thing to alleviate your workload, there is only one thing to do: complain about the workload to the ops chief, and possibly face the music..