Data impact on analyzing mysql table stats
If you are using the InnoDB engine for your tables #1 is relevant.  If you are using MyISAM, #3 is relevant.  But...

You should "never" have to run ANALYZE TABLE.  (There are exceptions, but they are so rare, that I will assume that the problem is elsewhere.)

Possible cause #1:  Your data has grown to be bigger than the cache (buffer_pool).  How big is the data?  What is the value of innodb_buffer_pool_size?  Are you using InnoDB?  How much RAM?

Possible cause #2:  Some queries have less than perfect indexes.  Set long_query_time=1; turn on the slowlog; wait a day; look in the slowlog to see what is slowest; come back for advice.