2 added 1116 characters in body
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Haskell, 72 bytes

p#s|let l@(h:t)!a|sum[1|e<-h:a,p e]>s=a:l![]|n<-a++[h]=t!n;_!a=[a]=(![])

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p#s     = (![])         -- main function that takes a predicate function 'p',
                        -- a size 's' and a input list without a name that is
                        -- directly passed as the first argument to function '!'
  let  l@(h:t)!a        -- function '!' is a local function (so that 'p' and 's'
                        -- are in scope). Takes a list 'l' of at least one element
                        -- 'h' (and 't' being the rest of the list) and an
                        -- accumulator 'a'
   |sum[1|e<-h:a,p e]>s -- if 'p' holds for more than 's' elements in 'h' and 'a'
     =a:l![]            --   put 'a' in front of a recursive call with the same list
                        --   'l' and an empty accumulator
   |n<-a++[h]           -- else bind 'n' to 'h' appended to 'a' and
     =t!n               --   call '!' again with 't' and 'n'
  _!a=[a]               -- base case for '!'. If the input list is empty, return
                        --   a singleton list with 'a' 

Haskell, 72 bytes

p#s|let l@(h:t)!a|sum[1|e<-h:a,p e]>s=a:l![]|n<-a++[h]=t!n;_!a=[a]=(![])

Try it online!

Haskell, 72 bytes

p#s|let l@(h:t)!a|sum[1|e<-h:a,p e]>s=a:l![]|n<-a++[h]=t!n;_!a=[a]=(![])

Try it online!

p#s     = (![])         -- main function that takes a predicate function 'p',
                        -- a size 's' and a input list without a name that is
                        -- directly passed as the first argument to function '!'
  let  l@(h:t)!a        -- function '!' is a local function (so that 'p' and 's'
                        -- are in scope). Takes a list 'l' of at least one element
                        -- 'h' (and 't' being the rest of the list) and an
                        -- accumulator 'a'
   |sum[1|e<-h:a,p e]>s -- if 'p' holds for more than 's' elements in 'h' and 'a'
     =a:l![]            --   put 'a' in front of a recursive call with the same list
                        --   'l' and an empty accumulator
   |n<-a++[h]           -- else bind 'n' to 'h' appended to 'a' and
     =t!n               --   call '!' again with 't' and 'n'
  _!a=[a]               -- base case for '!'. If the input list is empty, return
                        --   a singleton list with 'a' 
1
source | link

Haskell, 72 bytes

p#s|let l@(h:t)!a|sum[1|e<-h:a,p e]>s=a:l![]|n<-a++[h]=t!n;_!a=[a]=(![])

Try it online!