Yes it is fully synced. Before I rebooted it a couple of hours ago it had been running for months. And the blockheight matches mempool.space/testnet
Are you running a prune node? I suggest disable it if it set to prune.
What is your current node system specs? Are you in Ubuntu?
Can you try to edit the bitcoin.conf and add this "maxmempool=500" without qoutes or change it to 1000 then test make sure to restart bitcoind.
If you still having issue try adding this on the Bitcoin.conf file "mempoolexpiry=72" then restart it again and test.