There are several reason why this can happen. First, a longer than normal pause between words can trigger a new line. Second, if a new station starts sending, the the decoded text begins on a new line as an indication that a new transmission has begun. And third, if data is lost due to network congestion (most likely to happen in the case of a wireless internet connection), then the line break shows that one or more characters may be missing in the text.
No. In this regard, MorseMR is more forgiving than an actual closed-circuit telegraph system would be. If you leave your key open, other stations will still be able to use the wire.