The general rule is that you drop the ‑e, provided that it’s actually a silent one rather than forming part of an ee digraph as with agreeable, decreeable, disagreeable, foreseeable, and seeable.
You only otherwise have to keep a final silent ‑e when adding ‑able if it would (1) either change the pronunciation, or (2) it would cause a collision with an existing word that already means something else altogether different.
The first case, pronunciation shift, is for things like raceable or purgeable, where losing the ‑e would make the ‑ce or ‑ge switch from the “soft” version to the “hard” version due to the resulting ‑g‑ or ‑c‑ now being followed by an a rather than by an e, and ‑cable and ‑gable are pronounced quite differently.
The second case, a collision with an existing word, occurs with such pairs as pareable / parable, placeable / placable, probeable / probable, and spareable / sparable. Notice how placeable also has the first factor in play, as too would singeable / singable.
Beyond that, there is some slight variation in acceptable forms, such as both microwaveable / microwavable being attested. Normally however, you lose the ‑e. The OED2 attests 1555 words than end in ‑able but not in ‑eable, while only 123 that do actually end in ‑eable. That’s ration of nearly 13 to 1 in favor of more ‑able words without a preceding e.
Not excluding duplicates with alternate spellings, here are the ‑eable words from the OED2 plus quarterly supplements since 2000:
acknowledgeable decreeable haveable mingleable salvageable
acreable defaceable hireable mortgageable scribbleable
activeable delineable holeable nameable seeable
adduceable derangeable hopeable negligeable serviceable
advanceable disagreeable imageable noticeable shakeable
agreeable dischargeable immalleable packageable shapeable
allegeable discourageable impermeable pareable shareable
arrangeable displaceable inassuageable passageable sizeable
balanceable divorceable indulgeable peaceable skateable
batheable dyeable ineffaceable permeable sliceable
biteable effaceable influenceable pierceable spareable
blameable embraceable interchangeable placeable stageable
bounceable enforceable irremeable pledgeable strangleable
bridgeable exchangeable irreplaceable policeable swindleable
carriageable experienceable irretraceable poseable takeable
challengeable eyeable judgeable probeable tallageable
chanceable fleeceable knowledgeable pronounceable tameable
changeable foreseeable likeable purgeable tasteable
chargeable forgeable liveable raceable throttleable
chaseable garbleable lodgeable rateable traceable
chooseable gaugeable malleable reable vengeable
commenceable giveable manageable rebukeable voyageable
cuddleable gorgeable marriageable replaceable whistleable
damageable grazeable microwaveable ropeable
danceable hateable mineable saleable
As you see, there is also some tendancy to preserve the final e if in the original it’s there to make a so-called “long” vowel long. However, this doesn’t happen consistently enough to make a rule for them. However, for those cases there are a lot of alternate “sans”-e forms for those, like ropeable / ropable.
Perhaps a more interesting question — and certainly one with a more complicated answer — is how to know which words instead take ‑ible forms. There are 275 of these in the OED2, more than twice as many as ‑eable words. There are actual rules there, although they are a bit complicated for some people. That one I’ll leave for when it actually gets asked. :)