SPS2010 big list error: "Unable to execute query: Error 0x80131530"

You may fall into the situation where in a SharePoint Server 2010 farm, when a user of a specific group is trying to query a big list (>10000 items listed), he receives a Time out error.
If one of those users is added in another group, then he doesn't receive any such error.

If you check the ULS logs, you may find lines like the following:

w3wp.exe (0x05B8) 0x18C4 SharePoint Foundation General xxpm High Unable to execute query: Error 0x80131530 7114c45b-5454-4044-a996-f297eacef288
w3wp.exe (0x05B8) 0x18C4 SharePoint Foundation General 8e2s Medium Unknown SPRequest error occurred. More information: 0x80131530 7114c45b-5454-4044-a996-f297eacef288

In that case, at first ensure that you have installed at least Service Pack 2 for SPS2010. This should be enough.

If not, then it seems that the cause of this issue, is the fact that you have a quite big list and you are probably surpassing the list threshold limit.
There might be a big amount of data/items per list and also unique permissions. So, the SQL query appears to be quite performance intensive.
In SP 2010, when your query result is more than 10,000 items, as an environmental control, SP denies your request. For farm administrators this value is higher; 20,000 items. (Reference: https://technet.microsoft.com/en-us/library/cc262813.aspx)

You will need to check and if needed edit your settings in this list, like the List View Threshold, List View Lookup threshold, enable a daily time window for large queries, etc…
Some examples on the values to be used: 20000, 12, 13 hours.
These settings are located in Central Administration Application Management > Manage Web Applications > click the specific Web application > General settings > Resource Throttling.