it isn't a "known problem" per se with gpu with less than 2gb of ram, it is just that there isn't enough memory for using it on ethereum as ethereum use a large file (+1Gb) to compute the proof of work.
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DAG grows as blocks are added to the chain. If I remember correctly it is at 1.8GB right now, which means that 2GB cards are almost on their limit. But the switch to PoS will happen sometime in the near future, so it will not matter anyway.
Thanks, for the corection, perephrased to make it more accurate as a description of the issue :)