I'm looking into this, and I'm not yet sure why it does not always save the search in the order you create it. I was able to reproduce the issue the first time I tried, but subsequent times I saved the same set of search types, the order was preserved. What version are you on? Was that version upgraded from anything else?
To fix your current searches manually, you can modify the xml of the user attribute [WEBACCESS]SavedSeaches. EDIT: As Andrew noted below, there may be multiple attributes. See his post for more info. It's a good idea to back up your user attributes using "Export" before modifying them.
The user attribute should look something like this:
<?xml version="1.0" encoding="utf-8"?><SavedSearches><RepositorySearches Database="DBName"><Search Name="YourSearchName" BasicString="" SearchText="" SearchNames="" SearchFields="" SearchAnnotations="" SearchCustom=""><Attribute ID="Text"><Word1>YourTextSearchTerm</Word1></Attribute><Attribute ID="SearchFolder"><Item_0>1,RepoName\FolderPath</Item_0><CurrentFolder>0</CurrentFolder><Subfolders>1</Subfolders></Attribute><Attribute ID="Name"><String>YourDocumentName</String><Comparison>Exactly</Comparison></Attribute></Search></RepositorySearches></SavedSearches>
The order of the Attribute nodes determines the order the searches load in. Simply move everything between (and including) the <Attribute ID="Name"> and </Attribute> tags to before the <Attribute ID="Text"> tag, and the search should load in the correct order.
You should end up with something that looks like:
<?xml version="1.0" encoding="utf-8"?><SavedSearches><RepositorySearches Database="TheDangerZone"><Search Name="NameTextFolder" BasicString="" SearchText="" SearchNames="" SearchFields="" SearchAnnotations="" SearchCustom=""><Attribute ID="Name"><String>Name</String><Comparison>Exactly</Comparison></Attribute><Attribute ID="Text"><Word1>Text</Word1></Attribute><Attribute ID="SearchFolder"><Item_0>1,TheDangerZone\Brianna</Item_0><CurrentFolder>0</CurrentFolder><Subfolders>1</Subfolders></Attribute></Search></RepositorySearches></SavedSearches>