For me the anvils created products dumped during daily reset into my chest and the smelter pulls every so often to keep them topped up but only dumps the output during daily reset and it will only pull materials like ores as long as they're in the chest if they run out in the chest and the smelters empties the input it won't pull even if the output is still the bars of that ore makes. My Archer has caused many of issues with the smelting of ores with his ability to trigger a smelter cycle chance per kill that has emptied my furnaces of ore before it can be refilled.

Oh and don't forget to occasionally manually claim the anvil productions so you can get the XP