Tirex default tile expiration

This is a misunderstanding. The tirex-batch "expire" option,

   -e, --expire=TIME
           Expire time (seconds since epoch) for jobs. If it starts with '+',
           number of seconds added to current time.

specifies at what time a job should be removed from the queue if it hasn't been executed yet. It has nothing to do with the lifetime of a tile on disk. The default expire time is "never".

How long a tile is kept on disk is not something that Tirex decides; Tirex renders tiles when told so, full stop. Whether or not Tirex is told to render a tile, in a standard tileserver setup, is controlled by mod_tile, the Apache module responsible for delivering tiles. In a normal setup, a tile that is older than the last full planet import will be considered "old" and queued for re-rendering; in the absence of a file indicating the time of the last planet import, a tile older than 3 days will be considered "old". This is hard-coded here: https://github.com/openstreetmap/mod_tile/blob/6b9611aaf763f4f776d1fd363433aac7e25cb34b/src/store_file.c#L41

There are various ways to handle tile expiry. One option is setting the "last full import" timestamp to something last year, and then using the "dirty tile list" that osm2pgsql can produce to change the timestamp of every tile that needs re-rendering to 1970-01-01. This will then cause mod_tile to trigger a re-render if such a tile is reuquested. Alternatively, the re-render can be triggered immediately from the osm2pgsql output, but that would mean that even tiles that are rarely ever looked at but change often, would also be computed often.