An employer is not obliged to keep employing someone with recurrent health problems that mean they are not there sufficiently to do their job. However, you do need to go through the proper discipline (and if it comes to that, dismissal) process.
You need to know the employment legislation (which you don't seem to, so do take advice before you land in hot water). My understanding is that yes, holidays accumulate but do check thoroughly with a specialist, make sure you have good procedures and follow them.