EXPLANATION Notice that when we pronounce suffer, we stress the first syllable but when we pronounce admit, we stress the last syllable. If the last syllable of a word is stressed, we usually have to double the last consonant before adding a suffix (to stop the vowel sound from changing): thus, admit becomes admitted. (Otherwise, the vowel sound would change and the word would sound like ad-mite-ed.)
On the other hand, if the last syllable of a word is not stressed, we do not double the last consonant before adding a suffix: thus, suffer becomes suffering. (If we did double the r, the word would be pronounced sufferring.) Thus, for words of more than one syllable (that is, polysyllabic words) we double the final consonant before adding a suffix only if the syllable before that suffix is stressed.
(For the same phonetic reasons, the American spelling of words such as traveling and modeling is actually more logical than the conventional British spelling - travelling and modelling!)