We must first interpret this passage in the context of the two previous verses, in which we see that we do not approach the throne based upon our own merit, but that of our High Priest, Jesus the Christ. Thus, "boldly" does not mean recklessly or brazenly, but humbly and with confidence in the work of Christ. Under the old covenant, the people of Israel could not approach God directly. Only the high priest could come into the Holy of Holies, and then only once a year to make an atoning sacrifice to "cover" the sins of the people. Under the new covenant, Jesus, our ultimate High Priest, has atoned for our sins once for all (Heb 9:11-15), the veil has been torn (Mt 27:50-51), and we have free access to God.
Next, according to the Scriptures, even though we have free access to God, there are still some conditions which can obstruct our communication with Him. This brings us to one of the points of this article. During our group discussion, I pointed out that harboring unconfessed sin or disobedience (Jn 15:7), not asking in faith (Mk 11:23), asking with wrong motives (Ja 4:3) or for things contrary to the will of God (Jn 14:13-14, 1Jn 5:14-15), being inconsiderate of your family (1Pe 3:7) or several other conditions can hinder our prayers to God.
Another person then stated that we should avoid the "extreme" of approaching God with "a checklist". Now, we should avoid checklists in the sense of external obedience only, which is what I believe my friend was saying. We must however, not become so guarded against accusations of legalism that we avoid them altogether. When God doesn’t appear to be hearing our prayers, it could be that the timing isn’t right, or that he has something much better in mind for us, however, I see nothing extreme in taking a spiritual inventory (or checklist) in an attempt to determine other possible reasons such as mentioned above. In fact, the Bible not only exhorts us to petition God to examine us (Ps 139:23-24), we are also to examine ourselves (1Co 11:28-32).
In another instance, I just read a quote from a well-known pastor at a national conference a few weeks ago. In a speech on Christians’ need to "repent of religion", he stated that for religious people, Christianity becomes more of a "checklist of duties and behaviors", such as small group involvement, volunteering, taking a mission trip, and reading the Bible. In this case once again, these checklists and religious activities are inherently good. It is a hypocritical superficial focus, along with wrongful attitudes and motivations driving the activities that should be avoided.