Filter ListBox with TextBox in realtime

It's hard to deduct just from the code, but I presume your filtering problem born from the different aspects:

a) You need a Model of the data shown on ListBox. You need a colleciton of "Items" which you hold somewhere (Dictionary, DataBase, XML, BinaryFile, Collection), some kind of Store in short.

To show the data on UI you always pick the data from that Store, filter it and put it on UI.

b) After the first point your filtering code can look like this (a pseudocode)

var registrationsList = DataStore.ToList(); //return original data from Store

registrationListBox.BeginUpdate();
registrationListBox.Items.Clear();

if(!string.IsNullOrEmpty(SrchBox.Text)) 
{
  foreach (string str in registrationsList)
  {                
     if (str.Contains(SrchBox.Text))
     {
         registrationListBox.Items.Add(str);
     }
  }
}
else 
   registrationListBox.Items.AddRange(registrationsList); //there is no any filter string, so add all data we have in Store

registrationListBox.EndUpdate();

Hope this helps.