Flipping sniffer dog slips lead but doesn't give up (4,2)

'doesn't give up' is the definition.

'flipping sniffer dog slips lead' is the wordplay.
'flipping' says the letters should be written in reverse.
'sniffer' becomes 'nose' (**).
'slips lead' means to remove the first letter.
'dog' with its initial letter taken off is 'og'.
'nose'+'og'='noseog'
'noseog' written backwards gives 'GOES ON'.

'but' is the link.