Elasticsearch dies when Logstash attempts to write data

You need more hardware

Your raspi may be (considerably) under powered for your workload.

I'm in no way an Elasticstack expert, but I have set it up in several test scenarios and for limited/light production use. In my experience, while the initial setup requires relatively few resources, as the number of indexes grow the system generates significantly more disk IO and CPU load.

This is especially apparent after a restart while the system is recovering the shards. If your indexes are not too big, you could consider monthly buckets instead of the default daily buckets, which seems to help in this regard.