Why does it sometimes take a lot of time to show the pdf preview?
This may be due to errors in the document that you're working on -- the preview will only update when the document can successfully compile. Any errors thus prevent the preview from updating, and it will remain displaying the last successful compile until the errors are corrected.
You can see any errors in your document by moving your mouse over the word 'error' in the top right of the preview. For example, a common error is the need to put mathematical symbols in dollar signs, e.g. $\phi$ instead of just \phi.
If the pdf preview does not update even when the errors are resolved, please let us know and we'll take a look for you.