Excel seems to make heavy weather of 'Copying web  data to sheet'. I
got 'Not enough memory' messages for more than about 14 days.
The one line in your macro that on changing allowed me to get the
full 1 month's 6-minute data  quickly and without error was:
.WebSingleBlockTextImport = False
which I changed to:
.WebSingleBlockTextImport = True

A simple 'Text to columns' operation on the data (or all of column A)
using spaces as the delimiter restored the data cleanly to pretty
much the same state as your original macro and took no significant
time.
Tag something like this to the end of the macro:

Rows("1:39").Delete Shift:=xlUp
Columns("A:A").TextToColumns Destination:=Range("A1"), _
DataType:=xlDelimited,TextQualifier:=xlDoubleQuote, _
ConsecutiveDelimiter:=True, Tab:=False, _
Semicolon:=False, Comma:=False, Space:=True, _
Other:=False, FieldInfo _
:=Array(Array(1, 1), Array(2, 1), Array(3, 1), _
Array(4, 5), Array(5, 1), Array(6, 1), _
Array(7, 1), Array(8, 1), Array(9, 1), _
Array(10, 1), Array(11, 1), Array(12, 1))