plugins update doesn’t work..

Hi,
I really would appreciate help here.
So far when plugin update showed up, it was a matter just click on “update” and in few seconds all went fine and was done.
Now, when I click on “update” screen shows with line after line compiling like showing (I think) the whole content of that plugin, starting with “Error reporting set to E All” (it goes very fast..)
When it finishes, plugin becomes deactivated, actually vanishes from its place, going back to “installed plugin” area.
My updates are accumulating and I must correct that somehow. I am sure for some smart/ techie it might be easy matter, so please, someone help me.
Thank you so much in advance,
Regards,
Maya