Using 'live in the past' too often may imply you're not adaptable or forward-thinking, which can be negative in some contexts. While remembering good old days is nice, don't live in the past.
Pro Tip 2/3
Emotional Attachment
This phrase often suggests someone is emotionally attached to past events, which might prevent them from appreciating new experiences. He still wears his old varsity jacket and lives in the past.
Pro Tip 3/3
Negative Change Resistance
'Live in the past' can indicate a refusal to accept changes, especially when those changes are generally seen as positive. The company can't innovate if our CEO keeps living in the past.