VBA "out of memory" error when Excel consume only 70MB - vba

Question

Q: Why out of memory when my system have plenty of it left (and office is 64bit)
Q: Could it be that data when split cause such strange behavior?
Q: If splitting that string cause trouble then how to sanititize/restore it for just operations of storing/restoring that string?
Specs: Win 8.1 Pro + Office 2013 64bit, 8GB RAM in system
And here is the code, which just get single LARGE (~1-2MB) string, and split it into multiple cells, so that 32k chars per cell limit do not cause harm:
Public Sub SaveConst(str As String)
Dim i As Long
i = 0
' Clear prior data
Do While LenB(Range("ConstJSON").Offset(0, i)) <> 0
Range("ConstJSON").Offset(0, i) = ""
i = i + 1
Loop
Dim strLen As Long
With Range("ConstJSON")
.Offset(0, 0) = Left$(str, 30000)
i = 1
strLen = Len(str)
Debug.Print strLen
Do While strLen > i * 30000
.Offset(0, i) = Mid$(str, i * 30000 + 1, 30000)
Debug.Print i
i = i + 1
Loop
End With
End Sub
Right now Len(str) report ~270k characters, and i goes up to 4 iteration, and then "Out of memory" bug kick in.
Now that is n-th iteration of that bug in this place. But I have simplified/modified code so that it works sometimes. For exact same data set.
UPDATE:
Thx to Jean code, I'm confident that its SAVING partial string to the cell that cause that error.
.Offset(0, i) = Mid$(str, i * 30000 + 1, 30000)
Or
Range("ConstJSON").Resize(nPieces).Value2 = v
Both cause errors.
UPDATE 2:
I was saving that string to single cell without any fuss. But now that string grew too big to fit, splitting sometimes cause that error "Out of the memory".
Exemplary string:
[...]
""ebiZlecenias"":[{""id"":""91a75940-6d3e-06f8-bcf7-28ecd49e85f2"",""lp"":null,""name"":""ZLECENIE
GŁÓWNE"",""date_entered"":""2014-04-15
08:13:18"",""date_modified"":""2014-04-15
08:13:18"",""modified_user_id"":""2"",""budowa_id"":""8614aab5-29da-ffac-4865-e8c5913c729c"",""rodzaj"":""1"",""etap"":""1"",""data_akceptacji"":null,""opis"":null,""user_id"":null,""data_bazowa_od"":null,""data_bazowa_do"":null,""data_rzeczywista_od"":null,""data_rzeczywista_do"":null,""archiwalny"":null,""deleted"":null,""termin_raportowania"":null,""okres_raportowania"":null,
[...]

Answer 1

EDIT: I believe the problem with your specimen string is that some of the substrings begin with a "-". When that happens, Excel thinks the contents is a formula, and that is what causes the error. Pre-formatting the cell as text did not correct the problem, but preceding each entry with a 'single quote', which coerces the entry to text and will not show up except in the formula bar, seems to have corrected the problem in my macros, even when using your specimen string above as the "base" string.
EDIT2: What seems to be happening is that, if the string length is greater than 8,192 characters (the longest allowed in a formula), and also starts with a token that makes Excel think it might be a formula (e.g: -, +, =), the write to the cell will fail with an out of memory error EVEN IF the cell is formatted as text. This does not happen if the single quote is inserted first.
Below is some code that works on much longer strings.
The code below first creates a long string, in this case the string is slightly more than 100,000,000 characters, and then splits it into sequential columns. No errors:
Option Explicit
Sub MakeLongString()
Dim S As String
Const strLEN As Long = 100 * 10 ^ 6
Const strPAT As String = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
S = strPAT
Do
S = S & S
Loop Until Len(S) > strLEN
Debug.Print Format(Len(S), "#,###")
SplitString (S)
Debug.Print Range("a1").End(xlToRight).Column
End Sub
Sub SplitString(STR)
Dim R As Range
Dim strLEN As Long
Set R = [a1]
Dim I As Long
strLEN = Len(STR)
Do Until I > strLEN
R(1, I / 30000 + 1) = "'" & Mid(STR, I + 1, 30000)
I = I + 30000
Loop
End Sub
I just ran a test where the range being written to was a multi-cell range, and the target was set by the Offset method as you did, and it also ran to completion without error, filling in the first four rows.
Sub SplitString(STR)
Dim R As Range
Dim strLEN As Long
Set R = [a1:a4]
Dim I As Long
strLEN = Len(STR)
Do Until I > strLEN
R.Offset(, I / 30000) = "'" & Mid(STR, I + 1, 30000)
I = I + 30000
Loop
End Sub

Answer 2

This is worth a try: first split the string into an array, then slap that entire array onto the sheet at once.
Const pieceLength As Long = 3000
Dim s As String
Dim i As Long
Dim nPieces As Long
Dim v As Variant
s = ... ' whatever your string is...
nPieces = WorksheetFunction.Ceiling(Len(s) / pieceLength, 1)
ReDim v(1 To nPieces, 1 To 1)
For i = 1 To nPieces
v(i, 1) = Mid(s, (pieceLength * i) + 1, pieceLength)
Next i
Range("ConstJSON").Resize(nPieces).Value2 = v
I haven't tested your code, so can't say exactly what's wrong with it, but I know that writing to (or reading from) individual cells one at a time is slow and expensive; it's usually much better to read/write large swaths of cells to/from arrays, and manipulate the arrays (instead of the cells).