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In an x-ray tube, the atoms in the anode are ionized by incident electrons "knocking" their K-shell electrons out of orbit. Following this, an outer-shell electron decays to fill the vacancy. Now:
An atom remains ionized for a very short time (about $10^{-14}$ second) and thus an atom can be repeatedly ionized by the incident electrons which arrive about every $10^{-12}$ second. (NDT)
What causes the un-ionization, if there's another $10^{-12}$ second until the next incident electron arrives?
First, you are making the assumption that every incident electron causes a K-shell ionization event. Only about 0.1% of them do according to your reference. So the mean time between successive K-shell ionizations is closer to about 10^-9 seconds or 1000 times longer than the mean time between incident electrons.
Second, you are ignoring the space charge. When electrons are knocked out they don't just disappear. There are lots of them hanging around and available to back-fill the ejected electron.
