I know such lossless video splitter to support and split big video files, such as your mentioned TS file. It works fine with no audio missing problem. You can apply it fast trim any kinds of videos audios at 60X fast speed. Also, what I like most is its video editor to rotate, crop, watermark, effect and more.
Not sure if you have already owned such similar tool. However, if you often cut and edit multimedia files, you might as well get a cheap yet professional one in this special Thanksgiving offer.