Found out a few things: It seems during product indexing the amasty_feed_valid_products gets cleaned up. This causes the error we see in the backend because each iteration queries the table like this:
select * from amasty_feed_valid_products where feed_id=75 limit 2000,500
If the result is empty, because the indexer is just in progress of updating the table, the error will be thrown.
However, the Amasty Feed module supports a lock for the indexer. But that doesn't seem to be effective as the AJAX request will release the lock and the small time between the response and then new request from the browser seem to be enough to cause an error.
The cronjob shouldn't be effected by that. But the locking provider in env.php is maybe not effective. Maybe try to use database as locking provider:
'provider' => 'db',
'prefix' => null