I think I may have a possible solution.
First add the command to the embedded macro for the CompanyNameSearch control. After the SearchForRecord command add: GoToControl, CompanyName as suggested by Rick.
Then, instead of using FindNext in the "Next" command button, use :

SearchForRecord -  Object type and Object name leave blank
Record - next
Where condition - ="[CompanyName] = '" & [Screen].[ActiveControl] & "'"

It works for me ! Maybe Scott could let me know if this works for him as well ?
Course, the question still remains WHY it should be different in the first place ?

Also Rick : In the downloaded DB, I couldn't get the VBA to work on clicking the "Next" button. What I did was, write the above macro, convert it into VBA and replace it with what was on the buttons onclick event. Hey presto it worked !!

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Reply from Richard Rost:

Interesting. I'll play with it when I get a few minutes.