Why don't alkaline earth metals lose only one electron when they are ionized?
Magnesium can definitely exist as $\ce{Mg^{+}}$. Hence the availability of first ionization energy data for magnesium. 

The same goes for other metals; there are only uncommon valences, such as $\ce{Na^{3+}}$. 

If you had enough energy, you could make $\ce{Na^{4+}}$ if you wanted to. It would just cost, according to the table below, 9543 + 6912 + 4562.4 + 495.8 kJ/mol. 



I think your question is why isn't $\ce{Mg^{+}}$ more commonly encountered. That has to do with stability. Losing two electrons and becoming isoelectronic with a noble gas is more stable than having an unpaired electron. An unpaired electron is available for bond formation, and bond formation tends to be exothermic. 

If you want to read up on the +1 valence of magnesium, such as in $\ce{MgH}$, you can read more here:

http://bernath.uwaterloo.ca/media/24.pdf