Lettuces dying off

planted several pick and come again lettuce dotted in a flower bed with verbena.  One lettuce started to wilt and the stem where I had been cutting from had gone brown and slimey, so I dug it up.  Now another one has done same.  When I checked the roots they have gone whitey/grey.
The flowers are all ok.  It now looks as if the next one starting to do it.  They are spaced about 15" apart.  Whats going on?  ta.  Mrs Bouquet.

They don't like the heat much. Is there anywhere shady you could sow some more?