Making a publication go longer before becoming inactive will make your distribution database larger (for transactional replication), but it shouldn't really hurt anything as long as your distributor can handle the growth.
If the Subscribers have connectivity issues reaching the Distributor, there are several things that you can do. Each of those choices has different costs and benefits, so you need to find the one that works best for your situation.
If this is a simple dissemination of information (the subscribers only receive data, they never attempt to change it), then I'd suggest using snapshot replication. This isn't on ongoing process like Transactional replication, but Snapshot replication usually sends much less data over the network than Transaction replication does, and you can have much better control over the timing of the transmission so that it has less interferance with other processes using the network.
If you need to keep the Transaction replication, you may need to resort to a job that will periodically check to see if the distribution task is stopped and the subscriber is available, then restart the distribution task. Jobs are ideal for this because you can have a step attempt to do something that may fail catastrophically (in other words, cause the script to abort), but have the job continue on afterwards.
It would take considerable knowledge about your setup to find the "best" answer, but it shouldn't be hard to find a solution that you can live with.