Yes, Google is notorious for that, especially if you have a higher-ranking site. I have found that they usually drop for around a week or so shortly after being changed. Assuming that Google still considers your change to be relevant after your update, you should get back up close to where you were before shortly.
Having said that, I don't know if that applies to the first drop that you mentioned or not as that sounds more like you were affected by an update or something. The second drop sounds like a textbook example though.
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