Wait until they run out of mana or buy mana sucking items.  Also, if you can gauge the health of their shield, use a powerful burst damage attack to bust through and do extra damage so they lose some health before they have to shield again.  When QoT shields it is not the time to be using powerful burst damage attacks, wait 4 or 5 seconds and then unleash. 

a big problem i run into is playing against a QoT on any small map where she can just shield herself and her ally incessantly...against a good QoT in this situation the games lost (for me anyway).

Dear Newbie Regulus Player.. please MoTB the queen, mine her and beging your autofire destruction...sounds like you failed in trying to kill her with snipe..

If its mid end game the only abilities you'll be using as Reggie are MoTB and Mines after activating the wings.

Actually shield does not last forever.  Cast it once and stand still, it goes away, meaning it does go away over time.  The reason I say to wait 4 or 5 seconds though is if you think you've done about halfway damage and then start using some burst damage you can break through and do some damage to her actual health before she has a chance to recast it.  For instance, if you've done about 800 damage to a 1450 shield as tb, (you can actually mentally add the numbers as you are attacking) start using some burst damage like fireball, rain of ice, deep freeze, etc. and you will most likely break through to her health.  A plus is most QoT players do not stack much health at all.

Also, the shield recast timer makes it hard for her to continually shield both herself and an ally, one of them will always be open for attack.  Making QoT shield an ally is always a better move, as you can almost always kill her faster anyway due to her lower health.

I'm not sure, but I think that Mark of the Betrayer cast before QoT uses her shield makes it where the shield cannot cast and she just takes some damage.

It's happened to me before, at least I've always thought this was the cause. 

MoTB is damage to the Demigod and ALL its minions when they use an ability (like casting a new shield).  Against any Queen MoTB with Mines cast on top of her will burst enough damage to kill all her minions and your auto fire will finish her off as she's about 70% snared. 

MoTB also adds a snare effect and the mines maxed do as well...MoTB maxed is 800ish? and the mines are 600 each (thrown centered on her you get her with all three)

This does three things 1) a massive burst of damage to her, 2) kills all her shamblers (nada to mulch) 3) snares her real good.

Now not having any shamblers to mulch (for those that play this way) she will run to buy time for shield or shamblers or mulch shambler to finish their cooldown. 

You should also be shooting at about .8 sec intervals at this time or better She simply cannot outlast the DPS you should be laying down on her.

small correction Lugh: the highest levels mines (rank 4, Shrapnel Mines), deal 450 damage each. a triple blast will deal 1350 damage, which is 100 damage less than a full Rank 4 Bramble Shield. 

you're right about the rest of the stuff though, what you basically need to do is use the mines to burst down the shield then get your hits in with auto-attacks. two rounds of that is usually a kill.