Yes, having your solar blanket on most of the time will virtually eliminate carbon dioxide outgassing which is usually the main cause for rising pH (so having your cover on will virtually "freeze" your pH). Your TA is high so if you use your pool and keep the cover off, you will find a reasonably strong tendency for the pH to rise. So I suggest you simply remove your cover (during the day; keep it on at night to retain heat) and you should find your pH rising.
You could also follow Ben's Lowering Your Alkalinity procedure to lower your TA to around 80 so that when your cover is off you won't have such a large tendency to have pH rise.
Richard
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