Little Kenneth died, Saturday or Sunday (7)
I believe the answer is:
weekend
'saturday or sunday' is the definition.
'little kenneth died' is the wordplay.
'little' becomes 'wee' ('wee' can be similar in meaning to 'little').
'kenneth' becomes 'ken' (I've seen this in other clues).
'died' becomes 'd'.
'wee'+'ken'+'d'='WEEKEND'
(Other definitions for weekend that I've seen before include "Sat. and Sun." , "time off work?" , "See 21" , "couple of days" , "Occasional" .)