Can I use incomplete panel data for individuals if I control for fixed effects?

I’m trying to apply a Difference-In-Difference Model with monthly panel data on the words used in the Tweets of about 60 German politicians. Because of the way the Twitter API works, I can only read the last ~3200 Tweets of any given user, which means that there is no data for very active users the further back I want to go in time. I’m using controls for fixed effects and party membership. Say I want my time period to be within 01/2018-08/2021. There are some users that I do not have data on before 02/2018, 05/2018, 02/2019 etc. Do I need to throw out individuals with missing data within that period or am I controlling for that factor with fixed effects?