Its mostly related to the API restrictions that Twitter has put in place themselves, if you want more tweets, you may need to set up DM workflow to extract tweets and dump them into a file on an hourly basis, according to this is should be able to make 350 at most.
"Using the REST API? Applications are allowed to make 150 logged out (unauthenticated) requests to the REST API per hour, or 350 if you have allowed the application to act on your behalf (authenticated). Requests which count towards the rate limit are those which get information from Twitter for you to read. Requests which perform actions like tweeting, following and favoriting do not count toward this limit."
The wording implies that the limit to how many calls Omniscope can makes is on application basis too, so might not just be a user limit. One of the devs will have to check that and explain if this means that across all users.
IF you want to deal with large volumes, you may need to get access to an existing tweets mining product (most of these are paid services) or set up your own tweet mining bots (http://blog.mollywhite.net/twitter-bots-pt2/).
As Daniel said, there is a limit of requests you can make at a time, the Twitter block is configured to wait until the time limit is over to continue with the requests.
Twitter limits the number of tweets that you can request at a given time and in order to requests older tweets, you would need to configure Omniscope to repeatedly make requests.
"Keep in mind that the search index has a 7-day limit. In other words, no tweets will be found for a date older than one week."
Twitter also limits the number of search requests in a 15-minute window to 180 per authenticated user and up to 450 per authenticated app (IP of the request). Each request returning up to 100 tweets.
"Access to the Search API is measured by the IP address the request is coming from. In large offices and at events or conferences, it is common for many people to share the same IP address and in some of these cases, our rate limiting may be too strict."