If the 3 options you list, only one of them will automatically resume processing following a network outage. This is replication. In your environment, you would need to make sure that you set the appropriate properties on the distribution agent so that it is more resilient to network outages. The sort of options you need to consider include batch and transaction size and timeout durations.

SSIS packages are usually scheduled to run at particular time(s) of the day. So it the network is down, it won't automatically retry. It will fail if the network is down. The next time it is scheduled to run, is the next time it will attempt to replicate data.

WebServices, of themselves, do not do anything unless an application makes of request. Webservices are normally written so that you make a request (e.g. give me some data please). The webservices responds with the data that satisfies you request and then it stops processing. If you wrote the webservice to replicate data when you made the request, it would behave a bit like the SSIS package...it would attempt to connect, potentially fail, return some success or failure status and then go back to sleep.