Missing tweets in the home timeline shouldn’t be something that happens on a regular basis.
Are you backing out of the app using the back key?
Leaving the app via the home key or task switcher is also much more likely to leave gaps in your timeline vs. actually backing out so the app doesn't continue running in the background (you also won't get notifications if you don't back out).
Below you can find a simple diagram of how the gap works in the Twitter API (the feed that Twitter gives us to display tweets from Twitter in your TweetCaster client software). This shows why things work the way they do in the app currently.
It's important to note that it may not always be possible to receive every tweet from every account you follow. TweetCaster doesn't really "hold" tweets- we pull the requested data for your account for the API when the app is updated. Twitter don't give you all the data for your account at one time through the API. They have what they call "Gaps" and there may be time periods that you cannot fill based on when the app was installed and what tweets are available.
It is also worth noting that the home timeline can only go back 800 tweets. If you are getting a large gap of tweets, you could increase the "message to load" option in Settings to 100. That may help on that front.