Yes it is random. Over the years of studying draw history of actual draws I have not seen any hit skip pattern where it is consistant. Have hit skip patterns all up and down the history.
Tracking numbers in groups like v-tracs I find just a bit more in pattern recognition. Groups will have their comes and goes just like you mentioned. But that still makes groups random.

Will they correct themselves? Is there any data to suggest (approximate) how long it takes to make a correction?

I combine draws.
I looked thru history of tn v-tracs and it was rather difficult to find a hit skip pattern in box combos, exact order combos and exact pairs. Normally one would go by hit avg or hit median but that does not work to well either.
I am more of a hit skip pattern reader.
Where I did find some recognition was in v-trac sums on hit skip pattern. This would be something I would be working with when using v-tracs.
In the sum I am working with I would be looking at the hit skip pattern of each v-trac combo in that sum and decide from there.

Eample v-trac sum 10
v-trac sum 10 _____145, 235, 244, 344

Nov 5 2011 was the last draw entry in my file.
Structure search of TN3M&EVT.dmg: All Records   Printed: 02-15-2012
683 Records Found          683 Selected Records Printed           Page

Record     Date     P1 P2 P3 P4 Matched Skips
-----------------------------------------------------------------------------   4509   08/08/2011   3    4    3            1      12
   4510   08/09/2011   4    3    3            1       0
   4512   08/10/2011   2    5    3            1       1
   4521   08/15/2011   4    4    2            1       8
   4527   08/18/2011   4    1    5            1       5
   4530   08/19/2011   2    5    3            1       2
   4535   08/22/2011   4    5    1            1       4
   4557   09/03/2011   3    3    4            1      21
   4561   09/05/2011   2    4    4            1       3
   4567   09/08/2011   1    4    5            1       5
   4572   09/11/2011   4    1    5            1       4
   4577   09/14/2011   2    5    3            1       4
   4585   09/18/2011   4    5    1            1       7
   4601   09/27/2011   3    2    5            1      15
   4612   10/03/2011   4    2    4            1      10
   4615   10/04/2011   2    5    3            1       2
   4616   10/05/2011   2    3    5            1       0
   4617   10/05/2011   2    4    4            1       0
   4618   10/06/2011   5    1    4            1       0
   4619   10/06/2011   2    3    5            1       0
   4625   10/10/2011   4    2    4            1       5
   4634   10/14/2011   1    5    4            1       8
   4637   10/16/2011   5    1    4            1       2
   4645   10/20/2011   3    5    2            1       7
   4647   10/21/2011   2    5    3            1       1
   4660   10/28/2011   1    5    4            1      12
   4665   10/31/2011   5    4    1            1       4
   4669   11/02/2011   5    1    4            1       3

I made an error in copying the v-trac sum 10 combos. That 344 v-trac is not right. It should read 334 v-trac
Eample v-trac sum 10
v-trac sum 10 _____145, 235, 244, xxx 334

Out of this data taken for a yearly look see..I will just bet that there are some vtracs that didn't do so much. The 135 vtrac was really lacking last year in TN as well. They have vtrac 135 (straight) out 793 draws or something like that. I wish I would have written down those little things last year. They would have come in Handy this year.

I haven't been doing this very long Little, but I am quite frustrated because patterns that I have noticed from the past are most definitely NOT doing anything for me for the last few months.

I don't think TN drawings is random. For example take 3/10/12 and 3/11/12 eve draws 803 and 307 that is a pattern.
3/12/12 and 3/13/12 midday draws 045 and 640 again that is a pattern. TN does that alot and the payouts is low
but we can't seen to catch them doing it. We should be hanging them out to dry. Tonight i am betting they will pull
the 19 pair or 94 pair again.

We should not base anything conclusions on computer generated numbers. Heck, we shouldn't even track them.
There is order in chaos except when Tennessee's lottery gets involved. Then we also have the human manipulation of outcomes to produce the most profit for the state.