OLD has definitions for fixated, fixative, but not fixate. This suggests that fixate is not a normal, modern word that one can use in everyday speech or writing... Is this right?
Note: OxfordDictionaries has fixate. I find it strange.
As to OLD - I sent an Email to their contact address to inquire as to this discrepancy. Here is an excerpt from the reply:
This is simply a matter of frequency. The adjective fixated is found much more frequently in our corpus of 2.5 billion words of English than the verb, and the noun fixation is more common still.
It would seem they simply don't consider "fixate" common enough to include. However I hear this kind of thing commonly:
Try not to fixate on the details.
So in my view as a native speaker, fixate is a commonly used modern word. I guess if OLD is missing a word, just try another dictionary.
Remember that there is no arbiter of the English language. What words are part of the language is a matter of consensus among people who speak it. New words pop up, die off, get imported, or get redefined all the time - the dictionary is a resource for understanding, not a definitive guide to vocabulary.