"Update tblmkOpenClose set tblmkOpenClose.ChkRequestDate= '" & Me.txtChkRequestDate & "' Where CLAIMNBR='" & Me.txtCLAIMNBR.Value & "'"
You are forgetting to put ' ' around text values
I question why you aren't making dates of db type DateTime for ChkRequestDate, but that is your choice. The above seems to work.