On my computer, it has been setup to automatically delete shortcuts from the Start menu or desktop, when they are not being used for a while.
The problem is that sometimes I don't use programs for a little while but I might later on, and I'd like the shortcuts to remain.

How do I stop this from happening?

Are you using Windows XP? If you are, then it shouldn't be deleting the shortcuts, but putting them in a folder called "Unused Shortcuts" which sits on your Desktop.
If you click on that folder, all those shortcuts should be there.
You can turn this function off, but I'm not sure how cuz I like it and have never tried.

If you're not talking about Windows XP, ignore everything I just said.

Yes, sorry I forgot to mention that I am using Windows XP, and you're right that the files are not being deleted but removed from the shortcuts. I haven't got any 'unused shortcus' folder on my desktop though.

My computer asks me before it deletes them, I just tell it not to delete them.

I searched help and found this information, and followed the steps described. Although it shows how to remove desktop items, I think you might find that doing a little unchecking might work. I found a checkbox that says to clean up desktop every 60 days. Maybe if you uncheck that, it will stop the automatic cleanup. Hope this helps. I have not tried this, so this suggestion does not come with guarantees!

To remove unused desktop icons
Open Display in Control Panel.
On the Desktop tab, click Customize Desktop.
(This is where I found the checkbox to clean up desktop every 60 days)
Under Desktop cleanup, click Clean Desktop Now.
Follow the directions in the Desktop Cleanup Wizard.
Notes

To open Display, click Start, click Control Panel, and then double-click Display.
The Desktop Cleanup Wizard displays a list of the desktop icons that have not been used for 60 days or more, enabling you to remove those icons that you don't want on your desktop. You can retrieve icons you have removed by opening the Unused Desktop Shortcuts folder on your desktop.
Clear the Run Desktop Cleanup Wizard every 60 days check box if you don't want the wizard to run automatically every two months.
You can remove an individual desktop icon by right-clicking the icon and then clicking Delete.
To add or remove the icons for My Documents, My Computer, My Network Places, or Internet Explorer, select or clear those items under Desktop icons.

I have sorted out the desktop icons but I can't find where the files from All Programs on Start Menu went.

From what I can remember, these files are missing from the menus:

*Accessories: Calculator, Paint, Sound Recorder
*Games: All of them including Solitaire, Pinball, Freecell, SPider Solitaire and the Internet games etc.
*All Programs: Windows Movie Maker

I did a search on these files but the only one the computer found was Movie Maker, in Program Files so I can restore that. But all the other files were not found on the search and nor could I find them manually.

Does anyone know where these files may be loacted?

I am using Windows XP.

I couldn't find out where the Shortcuts go, but, perhaps if you do a search (through My Computer) for files called *.exe (the asterisk means anything) you'll get a list of all the executable files on your system, and, as Shortcuts are executable files you should be able to locate them if they are still 'there'! Hope this helps a little bit!

I have found Paint and Pinball...still looking for the others. I remember seeing some option that asks you if you want files to be compressed after an amount of time and that was ticked when I first got my laptop but now I can't remember where to locate that.
And it is not the one for the desktop which was mentioned above: 'Run desktop cleanup wizard evry 60 days'.

Calculator will be c:\windows\system32\calc.exe.

Edited to add: the games will be in c:\windows\system32 also. Solitaire is Sol.exe and minesweeper is winmine.exe. Hearts is mshearts.exe, and freecell will be freecell.exe. The sound recorder is sndrec32.exe and spider solitaire is spider.exe. As for the internet shortcuts, I am not sure where those will be found. Hope this helps!