There are 2 reasons I can think of that your control handles are disappearing: 1) You're mistaking the anchor point for the opposing control handle (they are pretty darn small; Adobe would do well to offer a preference to make 'em bigger). If you click an anchor point with the Convert tool, any handles will indeed disappear.
Or 2), your click is missing the control point, so you're de-sellecting the path. But that should only happen with a Selection tool, so it must be 1)
If you want both handles to move together, grab one with the white arrow. If they don't move together, THEN you'll need the Convert tool: click the anchor (handles disappear), and without letting go the mouse button, drag out a fresh pair of handles. Don't click again with Convert; switch back to the Direct Selection (white arrow) and grab a handle.
Tip: Leave the Pen tool selected, and access the Convert tool temporarily with Alt (Mac: Option); and the white arrow with Ctl (Mac: Command). (If that gets you the Black arrow, click A and then P for pen again, and Ctl/Com will get you the white arrow.)
You might wanna go through the Pen basics in a good Illustrator book, like Real World Ill. or The Ill. Bible etc.
If you don't have one, check out this good basic tutorial:
- pen tool - handles by dave at Nov. 11, 2002 8:02 am gmt (Rec'd 1)
- Re: pen tool - handles by Kacey Crouch at Nov. 11, 2002 1:12 pm gmt
- Re: pen tool - handles by dave at Nov. 12, 2002 8:18 am gmt
- Re: pen tool - handles by pbasswil at Nov. 14, 2002 8:15 am gmt
- Re: pen tool - handles by dave at Nov. 15, 2002 7:17 am gmt
- Re: pen tool - handles by pbasswil at Nov. 15, 2002 10:58 pm gmt