Are you using an error handler? If you're ignoring errors and try to name a sheet the same as an existing sheet or a name with invalid characters, it could be just skipping over that line. See the CleanSheetName function here
http://www.dailydoseofexcel.com/archives/2005/01/04/naming-a-sheet-based-on-a-cell/
for a list of invalid characters that you may want to check for.
Update
Other things to try: Fully qualified references, throwing in a Doevents, code cleaning. This code qualifies your Sheets reference to ThisWorkbook (you can change it to ActiveWorkbook if that suits). It also adds a thousand DoEvents (stupid overkill, but if something's taking a while to get done, this will allow it to - you may only need one DoEvents if this actually fixes anything).
Dim WS As Worksheet
Dim i As Long
With ThisWorkbook
Set WS = .Worksheets.Add(After:=.Sheets(.Sheets.Count))
End With
For i = 1 To 1000
DoEvents
Next i
WS.Name = txtSheetName.Value
Finally, whenever I have a goofy VBA problem that just doesn't make sense, I use Rob Bovey's CodeCleaner. It's an add-in that exports all of your modules to text files then re-imports them. You can do it manually too. This process cleans out any corrupted p-code that's hanging around.