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The problem is that your feature doesn't cross the date line from OpenLayers perspective, so your split line doesn't intersect your feature. Example from your data:

..., -178.475596 -81.673196, 156.248392 -81.611421,...

You go from -178 to 156, and this doesn't cross the date line from the OpenLayers perspective. Instead of splitting on the date line, you should split on your minimum X value.

// Build the splitting line based on the min and max coordinates of the vector to split
var minX = 999999999;
var minY = -20037508.34 // minimum value of the spherical mercator projection
var maxY = 20037508.34  // maximum value of the spherical mercator projection
//Extract the minimum X from the data as bounds seems to be rounded.
for(var i=0; i<satTrack.geometry.components.length; i++) {
    if(satTrack.geometry.components[i].x < minX)
        minX = satTrack.geometry.components[i].x;
}
var pointList = [
    new OpenLayers.Geometry.Point(minX, minY),
    new OpenLayers.Geometry.Point(minX, maxY)
];
var featDateLine = new OpenLayers.Feature.Vector(
    new OpenLayers.Geometry.LineString(pointList)
);

I've built an example here that successfully split your satellite track in 2 features: http://jsfiddle.net/6XJ5A/

Now to use the WKT with multiple line in your update, instead of using a straight line, you must go through the whole dataset and build your split line with all the coordinates that go across the dateline. By building small line inside a multiline, you can split on all the coordinates that should go across the dateline. Here's the updated example: http://jsfiddle.net/Jc274/

And the code:

// Build the splitting line based on the min and max coordinates of the vector to split
var pointList = [];
var lastPoint = satTrack.geometry.components[0];
//Extract the minimum X from the data as bounds seems to be rounded.
for (var i = 1; i < satTrack.geometry.components.length; i++) {
    if (Math.abs(satTrack.geometry.components[i].x - lastPoint.x) > 10000000) {
        pointList.push(satTrack.geometry.components[i]);
    }
    lastPoint = satTrack.geometry.components[i];
}

var lineList = [];
for(var i=0; i<pointList.length; i++) {
    lineList.push(new OpenLayers.Geometry.LineString([
        new OpenLayers.Geometry.Point(pointList[i].x, pointList[i].y-0.00001), 
        new OpenLayers.Geometry.Point(pointList[i].x, pointList[i].y+0.00001)
    ]));
}

var featDateLine = new OpenLayers.Feature.Vector(
new OpenLayers.Geometry.MultiLineString(lineList), null, split_style);

This will return you a splitted line on all the points that "cross" the dateline

Note that I also loop through the coordinates to remove the line that goes across the map to connect the 2 coordinates:

for (var i = 0; i < resultsDateLine.length; i++) {
    // Remove the first (or last) point of the line, the one that cross the dateline
    if (Math.abs(resultsDateLine[i].components[0].x - resultsDateLine[i].components[1].x) > 10000000) {
        resultsDateLine[i].removeComponent(resultsDateLine[i].components[0]);
    }
    if (Math.abs(resultsDateLine[i].components[resultsDateLine[i].components.length - 1].x - resultsDateLine[i].components[resultsDateLine[i].components.length - 2].x) > 10000000) {
        resultsDateLine[i].removeComponent(resultsDateLine[i].components[resultsDateLine[i].components.length - 1]);
    }
    features.push(new OpenLayers.Feature.Vector(resultsDateLine[i], null, style_array[i]));
}

Update: I updated the first example to only add the line that were split. I also updated the explanation accordingly. This approach is not bullet proof with the 24h satellite track you provided, but I'm working on it.

Update 2: I updated the second example. By using a multiline to split and looping through the result to remove extra coordinates added by the split, we get a set of features that never go across the dateline.