Is it normal to not be awarded perks at certain levels? There's been at least 3 levels where, after I distributed my points it went back to the game and did not give me the option to select a perk. Please tell me this is normal.

I'ts normal.

Obsidian decided to make it less like Fallout 3 and more like Fallout 1 and 2, where you don't get a new perk every level.

This is a good thing, as combined with other improvements (such as lower distribution of total skill points per level,) it makes it impossible to create a god-like character.

You get a new perk every-other level now.

Doing it every other level is normal. Now if it does it several times in a row something's wrong. The perk rate is 2 levels = 1 perk.

It's normal. It says so in the manual