EXPLANATION Our vague pronunciation of -ible and -able can make it difficult to decide which of the two suffixes to use to end a word. It is easier to decide which suffix to use once we know the reason for the difference.
If we examine allowable, for example, we can see that the first part of the word (allow) is a recognisable word; it does not need the addition of the suffix to turn it into a recognisable word. In such cases, the suffix to add is -able. Similarly, we have laughable, suitable, reasonable, treatable and so on. Because laugh, suit, reason and treat are English words in their own right, we add -able. Note that we also add -able if we have recognisable words that end in e, such as believe, achieve, desire, debate. We simply remove the e before adding -able (giving believable, achievable, desirable, debatable).
With permissible, by contrast, what comes before the suffix is not a recognisable English word; we do not pronounce permiss as a word in its own right. This is because it is Latin in origin. For such words, we add -ible. Similar words are edible, horrible and possible. We cannot say ed, horr or poss as stand-alone words; they are Latin roots.
Unfortunately, these rules don't work for all words. There are quite a few words where the Latin root forms a recognisable word. In such cases, the overriding factor is that it is based on Latin (or another foreign language) and so -ible is used. Words such as accessible, collapsible, defensible, digestible, fallible, reversible and sensible all require -ible even though we can say access, etc.