If you set a trailing stop and lose your server connection before the market moves in your favour by the number of points that you specified, the trailing stop loss order will not be placed.

If you set a trailing stop and lose server connection after the market moves in your favour, triggering the trailing stop, the stop loss order will not trail the market. It will work as a hard stop, fixed at the last price where the stop loss was at when you lost the connection.

To avoid the trouble, you can use VPS(virtual private network server) which constantly runs 24/7. VPS is normally used for running EAs(trading programs) so you can save the troubles like this.

But if the MT4 is down for a moment, all EAs and trailing stops will be stopped. So it’s better you monitor the positions/orders in your account at all times.

Although, cTrader has got trailing stop option in its trading server. Meaning that unlike MT4 which has information of trailing stop orders in the trading platform only, cTrader will have the order information directly to its trading server.

This enables trading stop order even when your cTrader account is not logged in or the platform itself is closed.

Moving from MT4 to cTrader might solve the trouble in this case for you.