Given a list, how can I perform some transformation only on sub-lists whose each two elements satisfy a binary predicate?

If we need to remember the difference between the 'a's and the rest, let's put them in different branches of an Either. In fact, let's define a newtype now that we are at it:

{-# LANGUAGE DeriveFoldable #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE ViewPatterns #-}

import Data.Bifoldable
import Data.Char
import Data.List

newtype Bunched a b = Bunched [Either a b] deriving (Functor, Foldable)

instance Bifunctor Bunched where
  bimap f g (Bunched b) = Bunched (fmap (bimap f g) b)

instance Bifoldable Bunched where
  bifoldMap f g (Bunched b) = mconcat (fmap (bifoldMap f g) b)

fmap will let us work over the non-separators. fold will return the concatenation of the non-separators, bifold will return the concatenation of everything. Of course, we could have defined separate functions unrelated to Foldable and Bifoldable, but why avoid already existing abstractions?

To split the list, we can use an unfoldr that alternately searches for as and non-as with the span function:

splitty :: Char -> String -> Bunched String String
splitty c str = Bunched $ unfoldr step (True, str)
  where
    step (_, []) = Nothing
    step (True, span (== c) -> (as, ys)) = Just (Left as, (False, ys))
    step (False, span (/= c) -> (xs, ys)) = Just (Right xs, (True, ys))

Putting it to work:

ghci> bifold . fmap func . splitty 'a' $ "aaassddddfaaaffddsssadddssdffsdf"
"aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD"

Note: Bunched is actually the same as Tannen [] Either from the bifunctors package, if you don't mind the extra dependency.

You could classify the list elements by the predicate before grouping. Note that I’ve reversed the sense of the predicate to indicate which elements are subject to the transformation, rather than which elements are preserved.

{-# LANGUAGE ScopedTypeVariables #-}

import Control.Arrow ((&&&))
import Data.Function (on)
import Data.Monoid (First(..))

mapSegmentsWhere
  :: forall a. (a -> Bool) -> ([a] -> [a]) -> [a] -> [a]
mapSegmentsWhere p f
  = concatMap (applyMatching . sequenceA)  -- [a]
  . groupBy ((==) `on` fst)                -- [[(First Bool, a)]]
  . map (First . Just . p &&& id)          -- [(First Bool, a)]
  where
    applyMatching :: (First Bool, [a]) -> [a]
    applyMatching (First (Just matching), xs)
      = applyIf matching f xs

    applyIf :: forall a. Bool -> (a -> a) -> a -> a
    applyIf condition f
      | condition = f
      | otherwise = id

Example use:

> mapSegmentsWhere (/= 'a') (reverse . map toUpper) "aaassddddfaaaffddsssadddssdffsdf"
"aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD"

Here I use the First monoid with sequenceA to merge the lists of adjacent matching elements from [(Bool, a)] to (Bool, [a]), but you could just as well use something like map (fst . head &&& map snd). You can also skip the ScopedTypeVariables if you don’t want to write the type signatures; I just included them for clarity.

There are other answers here, but I think they get too excited about iteration abstractions. A manual recursion, alternately taking things that match the predicate and things that don't, makes this problem exquisitely simple:

onRuns :: Monoid m => (a -> Bool) -> ([a] -> m) -> ([a] -> m) -> [a] -> m
onRuns p = go p (not . p) where
    go _ _ _ _ [] = mempty
    go p p' f f' xs = case span p xs of
        (ts, rest) -> f ts `mappend` go p' p f' f rest

Try it out in ghci:

Data.Char> onRuns ('a'==) id (reverse . map toUpper) "aaassddddfaaaffddsssadddssdffsdf"
"aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD"

Here is a simple solution - function process below - that only requires that you define two functions isSpecial and func. Given a constructor from your type SomeType, isSpecial determines whether it is one of those constructors that form a special sublist or not. The function func is the one you included in your question; it defines what should happen with the special sublists.

The code below is for character lists. Just change isSpecial and func to make it work for your lists of constructors.

isSpecial c = c /= 'a'
func = reverse . map toUpper

turn = map (\x -> ([x], isSpecial x)) 

amalgamate []  = []
amalgamate [x] = [x]
amalgamate ((xs, xflag) : (ys, yflag) : rest)
   | xflag /= yflag = (xs, xflag) : amalgamate ((ys, yflag) : rest)
   | otherwise      = amalgamate ((xs++ys, xflag) : rest)

work = map (\(xs, flag) -> if flag then func xs else xs)

process = concat . work . amalgamate . turn

Let's try it on your example:

*Main> process "aaassddddfaaaffddsssadddssdffsdf"
"aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD"
*Main> 

Applying one function at a time, shows the intermediate steps taken:

*Main> turn "aaassddddfaaaffddsssadddssdffsdf"
[("a",False),("a",False),("a",False),("s",True),("s",True),("d",True),
("d",True),("d",True),("d",True),("f",True),("a",False),("a",False),
("a",False),("f",True),("f",True),("d",True),("d",True),("s",True),
("s",True),("s",True),("a",False),("d",True),("d",True),("d",True),
("s",True),("s",True),("d",True),("f",True),("f",True),("s",True),
("d",True),("f",True)]
*Main> amalgamate it
[("aaa",False),("ssddddf",True),("aaa",False),("ffddsss",True),
("a",False),("dddssdffsdf",True)]
*Main> work it
["aaa","FDDDDSS","aaa","SSSDDFF","a","FDSFFDSSDDD"]
*Main> concat it
"aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD"
*Main> 

We can just do what you describe, step by step, getting a clear simple minimal code which we can easily read and understand later on:

foo :: (a -> Bool) -> ([a] -> [a]) -> [a] -> [a]
foo p f xs = [ a
         | g <- groupBy ((==) `on` fst) 
                      [(p x, x) | x <- xs]  -- [ (True, 'a'), ... ]
         , let (t:_, as) = unzip g          -- ( [True, ...], "aaa" )
         , a <- if t then as else (f as) ]  -- final concat

         -- unzip :: [(b, a)] -> ([b], [a])

We break the list into same-p spans and unpack each group with the help of unzip. Trying it out:

> foo (=='a') reverse "aaabcdeaa"
"aaaedcbaa"

So no, using == 'a' is avoidable and hence not especially good, introducing an unnecessary constraint on your data type when all we need is equality on Booleans.