I'm having difficulty with understanding this phrase:
sorry, I've been in a fairly deep recently
Is this statement cut off as not making greater sense to me? That was a response to my message.
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To be "in deep" can be understood as:
inextricably involved in or committed to a situation. "He knew that he was in deep when his things began to proliferate in her apartment"
Your sentence looks like a variation on it. Sometimes, a "strong" or negative word is omitted in spoken sentences, which in this situation could have been depression, as suggested, or illness, trouble.
Source: Oxford dictionaries