David Seal posted the following "sporadic solutions" for reverse-sum 
iterations in the Usenet Newsgroup rec.puzzles in January of 1996:

 "Base 4:
    1033202000232(n 2s)2302333113230
      After 6 iterations, becomes same thing with n increased by 3.
  Base 11:
    1246277(n As)A170352495681825A5026571A506181864A5143171(n 0s)0872542
      After 6 iterations, becomes same thing with n increased by 1.
 Base 17:
 10023AB83E3B983CFGEC556G4G010(n 0s)0FGCG10FG505GF020CGF(n Gs)GG11G4F655D
    DGGB299B3D38BB320G
      After 6 iterations, becomes same thing with n increased by 1.
  Base 20:
    There is a >200 digit number of the same general form which grows
    indefinitely without ever producing a palindrome, but I'm not going
    to try to transcribe it here!
  Base 26:
    1N5ELA6C(n Ps)P6E7(n 0s)0D59ME5N
      After 4 iterations, becomes same thing with n increased by 1."


Here are representative cycles corresponding to each of these solutions:

Base 4, period 6

 0        103320200023 22 302333113230
 1        202232133233 11 223001203131
 2       100020030022 123 221333101333
 3      103312202321 1111 102023122000
 4      110200123122 2222 231232001301
 5      213301021321 1111 113213003312

 6     103320200023 22222 302333113230
 7     202232133233 11111 223001203131
 8    100020030022 122223 221333101333
 9   103312202321 1111111 102023122000
10   110200123122 2222222 231232001301
11   213301021321 1111111 113213003312

12  103320200023 22222222 302333113230


Base 11, period 6

 0      1246277 a a170352495681825a5026571a506181864a5143171 0 0872542
 1      3698a48 0 0883768431399986541a1092545899a41337673890 a 8498963
 2      7286895 a 1757424762898860994812839a1688872685237661 0 5996816
 3     1246277 a a331374a51557661297853458882266745249484123 0 0872542
 4     3698a48 0 2546113376a23184075296a356a3923196843105462 a 8498963
 5     7286895 a 509012685283646802a6928602a8636492476220905 0 5996816

 6    1246277 aa a170352495681825a5026571a506181864a5143171 00 0872542
 7    3698a48 00 0883768431399986541a1092545899a41337673890 aa 8498963
 8    7286895 aa 1757424762898860994812839a1688872685237661 00 5996816
 9   1246277 aa a331374a51557661297853458882266745249484123 00 0872542
10   3698a48 00 2546113376a23184075296a356a3923196843105462 aa 8498963
11   7286895 aa 509012685283646802a6928602a8636492476220905 00 5996816

12  1246277 aaa a170352495681825a5026571a506181864a5143171 000 0872542


Base 17, Period 6

 0      10023ab83e3b983cfgec556g4g010 00 0fgcg10fg505gf020cgf gg gg11g4f655ddggb299b3d38bb320g
 1     10025f52c00f41afcfdb0ac544020 gg ggfbd11gf4565ef21dceg 00 0021444bb1bdfbeb23f0gc34e5210
 2     1128328fb0g16d8abc7cc4g985221 00 geb7e40e3aab4dg3f8bef gg 02258a04bd8cba7c71f1be9327211
 3     224f561d52e2e8g467g96902ga442 00 fc5gc80a85448ag8cg6ce gg 144b02g978g863g8d3e26d055f422
 4     449dab29b5b6b0f7cgg0e1g504884 00 d7cg8003g98a04008fc8c gg 3894g501e1ffc8g0a6b4c91bbd844
 5     891a55426a5d41eg8fe2b2gag90g8 00 8g8eg0080302g7010f7g8 gg 8008gag3b2ff7ge14d5a71465a088

 6    10023ab83e3b983cfgec556g4g010 000 0fgcg10fg505gf020cgf ggg gg11g4f655ddggb299b3d38bb320g
 7   10025f52c00f41afcfdb0ac544020 ggg ggfbd11gf4565ef21dceg 000 0021444bb1bdfbeb23f0gc34e5210
 8   1128328fb0g16d8abc7cc4g985221 000 geb7e40e3aab4dg3f8bef ggg 02258a04bd8cba7c71f1be9327211
 9   224f561d52e2e8g467g96902ga442 000 fc5gc80a85448ag8cg6ce ggg 144b02g978g863g8d3e26d055f422
10   449dab29b5b6b0f7cgg0e1g504884 000 d7cg8003g98a04008fc8c ggg 3894g501e1ffc8g0a6b4c91bbd844
11   891a55426a5d41eg8fe2b2gag90g8 000 8g8eg0080302g7010f7g8 ggg 8008gag3b2ff7ge14d5a71465a088

12  10023ab83e3b983cfgec556g4g010 0000 0fgcg10fg505gf020cgf gggg gg11g4f655ddggb299b3d38bb320g


Base 26, Period 4

 0        1n5eLa6c pp p6e7 00 0d59me5n
 1        p2kb4fjd 00 6kL6 pp cjg5ak2o
 2       1n5eLa6c pp pdgfd 00 0d59me5n
 3       p2kb4fjd 00 d373c pp cjg5ak2o

 4      1n5eLa6c ppp p6e7 000 0d59me5n
 5      p2kb4fjd 000 6kL6 ppp cjg5ak2o
 6     1n5eLa6c ppp pdgfd 000 0d59me5n
 7     p2kb4fjd 000 d373c ppp cjg5ak2o

 8    1n5eLa6c pppp p6e7 0000 0d59me5n