Curious - they should appear at both ends of the audio clip when you skim over it.
Have you tried trashing your preferences?
Faults like this can often be fixed by clearing out FCP X's preferences (for some reason, they get knotted up from time to time).
Download Digital Rebellion's Preference Manager (free, simple to use, and quite safe).
With Pref Manager, you can backup the Prefs first, then if trashing makes no difference, you can restore all your settings.
If you trash them and don't restore them, you will need to go over all your FCP X settings again, so it's a great idea to backup Preferences from time to time when FCP X is working well, then you can ditch the bad prefs and restore from your (Digital Rebellion) backup.
Can't guarantee it, but it's worth a try.
I found a workaround last night (not a solution). I used the Blade to cut off the beginning of the audio, which forced a new handle to appear on the righthand clip, which I then moved (in case it disappeared again!), deleted the new, smaller lefthand clip and then stretched the remaining clip back out to the left.
It's not great, but it got me out of a spot
Incidentally, does anyone know how to move the audio handles when they're hiding behind a transition? It's really annoying! I usually end up deleting the transition just so I can get to the handles, and then readding it again!