Why a pdf document with embedded fonts can be copied but is not searchable in pdf reader

Question

I am writing a pdf files with embedded subset fonts. As required, I am including the ToUnicode and CIDSet objects. To test, I created a simple PDF with two Hebrew characters. I can select the two characters and copy to the clipboard, and paste it properly into another application such as Word. But I am not able to search for a word containing these two characters. Adobe Reader (or Acrobat) displays the message that the word was not found. So in essence, I have created a PDF document which can be copied properly, but is not searchable. Any idea what I might be missing when creating the document?
Additional information: 1. The file in question is a minimal file with just two characters. I have tested with many such files in many different languages including English. None of the files are searchable. 2. Curiously, if I search for the letter 'e', Adobe reader highlights an incorrect word, even if the letter 'e' does not exists in the file. 3. Adobe acrobat is also not able to search within this file, however when I save the file to another disk file, the saved file now is searchable. I confirmed that the major objects such as the font-file, ToUnicode object, CID object, and the font description objects are the same in the saved file. However, one of the font object is brought up closer to the top of the file. 4. FoxIt is able to search these files properly.
5 0 obj
  <</Filter /FlateDecode /Length 115>>
  stream
        q 0.750000 0 0 0.750000 0.000000 792.000000 cm
        q q q 0.160000 0.000000 0.000000 0.160000 0.000000 0.000000 cm
        BT /F0 100.000000 Tf 0 g 750.000000 -690 Td[<02B0>] TJ 35.000000 0 Td[<02B9>] TJ ET Q
        Q
        Q
        Q
endstream
endobj
10 0 obj
<</FontName/AAAAAA+ArialUnicode/CIDSet 9 0 R /Ascent 905/CapHeight 905/Descent -212/FontFamily(Arial)/Flags 32/FontBBox [0 -212 1000 905]/ItalicAngle 0/StemV 0/FontFile2 7 0 R/Type/FontDescriptor>>
endobj
11 0 obj
<</BaseFont/AAAAAA+ArialUnicode/CIDToGIDMap/Identity/CIDSystemInfo <</Ordering(Identity)/Registry(Adobe) /Supplement 0>> /FontDescriptor 10 0 R/Subtype/CIDFontType2/Type/Font>>
endobj
12 0 obj
<</Subtype/Type0/BaseFont/AAAAAA+ArialUnicode/Encoding/Identity-H/DescendantFonts [11 0 R]/ToUnicode 8 0 R/Type/Font>>
endobj
8 0 obj
  <</Filter /FlateDecode /Length 252>>
  stream
        /CIDInit /ProcSet findresource begin
        12 dict begin
        begincmap
        /CIDSystemInfo
        << /Registry (Adobe)
        /Ordering (UCS) /Supplement 0 >> def
        /CMapName /Adobe-Identity-UCS def
        /CMapType 2 def
        1 begincodespacerange
        <0000> <FFFF>
        endcodespacerange
        3 beginbfchar
        <0000> <0000>
        <02B0> <05E0>
        <02B9> <05E9>
        endbfchar
        endcmap
        CMapName currentdict /CMap defineresource pop
        end
        end
endstream
endobj

Answer 1

I figured the app might have that ability - considering you can add text, highlight, add a signature, annotate and draw - so my thought was why not delete a page, or rearrange for that matter?.. That should be an option, this way we don't have to export to one of the other apps to delete or rearrange..
Thanks for the help, Bernd.
BTW if anyone is looking - PDF Max can do all of the above and delete and rearrange. With PDF Splicer you can delete and rearrange as well, but it has no other features.
And as for Steve Werner whose comment was deleted after it got to my inbox, it is much more than a Reader, as you can plainly see from the amount of tasks the Reader app can do above.