Six inquiries in 24 months shouldn't be a problem at all if they're reasonably spread out during that time (i.e. no big increase in inquiries in the last four moths or so). I don't know that there are any published thresholds of what numbers Barclays considers too many, but they do seems to give more weight to that number than some other lenders.

If you do get an online denial, do take the time to call recon, and let them ask about WHY you had inquiries, or why you want the card, or why you carry a balance, or why you have so many lines open with no balance, etc etc - they just really seem to want to get a fully picture of your credit profile; but like I mentioned a bit earlier, they've always approved me after having that conversation.

My wife has a younger credit profile, and they have denied her a couple times (twice I think), and even recon couldn't say exactly why, just give it time and try again - but she finally got auto-approved on her most recent attempt earlier this year.