Actually, different clauses of the Constitution are in conflict, and it is silent in the case of incapacity to serve.
For reference:
17th A: "When vacancies happen in the representation of any State in the Senate, the executive authority of such State shall issue writs of election to fill such vacancies: Provided, That the legislature of any State may empower the executive thereof to make temporary appointments until the people fill the vacancies by election as the legislature may direct."
Art.I, Sec. 5:"Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members,...
Each House may determine the Rules of its Proceedings, punish its Members for disorderly Behaviour, and, with the Concurrence of two thirds, expel a Member."
Art. V: "...and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate."
The question then arises: does a Senator who is incapable of providing "equal suffrage" constitute a "vacancy" per the 17th A., or can the Senate judge an incometent member to be "qualified" for membership? Are the grounds for expelling to be only "disorderly behavior", or is incapability grounds?
If this is pushed, it will be a USSC case.
A vacancy is not created by illness of a Senator only by actual death or resignation. Thus, the "equal sufferage" clause does not come into play. Effective representation does not apply either. There is precedent for long terms of absence by ill Senators.