One approach is something like the following:

Manipulate[
 Module[{nb},
  nb = CreateDialog[{TextCell["Computing..."], 
     TextCell[
      ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]], 
     TextCell["Click OK to close"], DefaultButton[]}];
  Pause[3];
  NotebookClose[nb];
  u],
 {u, 0, 1},
 ContinuousAction -> False,
 SynchronousUpdating -> False]

Note the ContinuousAction -> False option setting that serves to keep the computation from starting until you let go of the mouse button after moving the slider to the desired position.

By the way, the example in the documentation for SynchronousUpdating is not correct since it uses Pause[6] in the Manipulate example. However,

In[6]:= Options[$FrontEnd, DynamicEvaluationTimeout]

Out[6]= {DynamicEvaluationTimeout -> 6.}

So the example in the documentation for SynchronousUpdating does not show the issue. A better example would be

Manipulate[Pause[7]; x, {x, 0, 1}]

I submitted a documentation bug report for this...

The likely reason is that the computation is taking so long. Manipulate (and various other dynamic things in Mathematica such as Buttons) is set up to time out after a system-specified number of seconds (5 seconds for Manipulate). The main design reason for this is that things that are expected to respond quickly should, as a general rule, not take a long time to respond. Read the documentation on the SynchronousUpdating option to Manipulate to get a sense of this for Manipulate. And therefor try setting

SynchronousUpdating->False

in your Manipulate to see if that makes a difference in the behavior. Let me know what happens..>!