Using 1.10.15b datatables (no way to upgrade now) for a day it work perfect, save/load state. After while, mostly next date state reset to default. Checked server side database, it contains proper values.

Any direction for investigation?

"stateSave": true,
                "colReorder": true,
                "stateSaveParams": function (settings, data) {
                    var colNames = [];
                    for (var colIndex = 0; colIndex < settings.aoColumns.length; colIndex++) {
                        var colName = $(settings.aoColumns[colIndex].nTh).attr("name");
                        colNames.push(colName);
                        data.columns[colIndex].sWidth = settings.aoColumns[colIndex].sWidth;
                        data.columns[colIndex].sWidthOrig = settings.aoColumns[colIndex].sWidth;
                    }

                    for (var colIndex = 0; colIndex < data.columns.length; colIndex++) {
                        data.columns[colIndex].name = colNames[colIndex];
                    }
                    data.instance = settings.sInstance;
                    data.state = "save";
                    data.ColReorder = undefined;
                },
                <% if (!clipped) {%>
                "stateSaveCallback": function (settings, data) {
                    try {
                        var columnsInfo = JSON.stringify(data);
                        $.ajax({
                            type: "POST",
                            url: "search.do?jsm=getSettings",
                            data: {instance: form.instance, settings: columnsInfo},
                            async: false
                        });

                        if (isPageChecked(form)) {
                            $(form.form + ' .dataTables_scrollHeadInner th :checkbox').attr('checked', true);
                        } else $(form.form + ' .dataTables_scrollHeadInner th :checkbox').attr('checked', false);
                    } catch (e) {
                        console.error(e)
                    }
                },
                "stateLoadCallback": function (settings, callback) {
                    var data = null;
                    try {
                        $.ajax({
                            type: "GET",
                            url: "search.do?jsm=getSettings",
                            async: false,
                            success: function (json) {
                                json.state = "load";
                                data = json;
                                if (callback)
                                    callback(json)
                            }
                        });
                    } catch (e) {
                        console.error(e)
                    }

                    return data;
                },