Depends on if it is follow up from a call, or if you are prospecting into a list.
If the person has shown some interest, but is not responding, you can put them on a drip list to stay front of mind. First send them a note letting them know you will no longer follow up personally, but you are going to put them on the drip list. Sometimes this spurs people to respond with a positive as they see you are frustrated, others will respond and ask you not to put them on the list.
If you are prospecting, the key is to have a very targeted list of folks you KNOW should be interested. A campaign to a good list should include 10-13 "touches." These touches are a series of emails and voicemails that are each a little different and offer some little nugget of info. It takes on average 10 times before people respond. If your value is good, and your list targeted, most people will appreciate the persistence.