The reality is you do not have to accept people being off without a good reason.
You can investigate an employee's capability to work if they do not seem to be able to perform at the right level without a valid reason as long as what you do is proportionate, documented, fair and consistent with actions taken in same/similar cases.
Points to also consider:
- are there any underlying management issues that could be a contributory factor in this person illness?
- could the employee have an underlying condition that you simply do not know about?
Look at things with an open mind, seek a professional medical opinion and investigate the matter properly as part of a formal process.