Theo mình nghĩ thì đây là giải quyết một vấn đề đến cùng dù có khó khăn đi chăng nữa thì vẫn theo đuổi và tìm cách để giải quyết nó.

i think you can translate closure as finishing, ending, completing here, so that "concept of successful closure" is like understanding that however this thing ends will be like they wanted it to.

successful closure in mind = đồng thuận cao (trong quyết định vấn đề) / đồng thuận cao (trong nhận thức) / đồng thuận cao (trong tâm niệm)

Closure:
settlement, resolution, (something settled or resolved; the outcome of decision making) "they finally reached a settlement with the union"; "they never did achieve a final resolution of their differences";

consensus in mind

Consensus:
agreement in the judgment or opinion reached by a group as a whole"those rights and obligations are based on an unstated consensus";
http://wordnetweb.princeton.edu/perl/webwn?s=consensus
A consensual agreement or win-win outcome of collaborative problem-solving. A consensus implies that debate has taken place, the solution is generally accepted rather than a grudging compromise, and that agreement is deep-rooted enough that it can stand for some time without need to revisit the issue;
http://www.eubios.info/biodict.htm#c
A form of decision-making requiring all parties to agree completely with the issue(s) after extensive discussion and deliberation. Consensus occurs when individuals feel they have been able to express themselves, have been listened to and can support the final group decision, although levels of support may vary.
http://learningtogive.org/youthworkers/03glossary.asp
A decision-making process which results in decisions approved of by everyone involved. It is a powerful way to improve communication, and deal with change, scarcity, diversity, and power imbalances.
http://managingwholes.com/glossary/c.htm
To be adopted by consensus when all the members of the organ tasked with taking the decision give their tacit consent. No voting takes place. Consensus differs from unanimity which is an explicit agreement, resulting from a vote in which all members cast a vote. ...
http://www.franceonu.org/france-at-the-united-nations/the-un...

"đồng thuận cao"
http://hatinhcity.gov.vn/ArticleDetail/21/470/Trien-khai-pho...
http://thixaquangtri.gov.vn/default.aspx?TabID=100&modid=571...
http://e-info.vn/vn/index.php/chinh-tri/48787-chiến-lược-phá...
http://thethaovanhoa.vn/van-hoa-toan-canh/giai-thuong-hoi-nh...
http://www.tuyengiao.vn/Home/Quocte/sukienvabinhluanqt/42685...


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Note added at 16 hrs (2013-03-08 07:14:45 GMT)
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Consensus in mind:
The context is about a win-win outcome of collaborative problem-solving or decision-making requiring all parties to agree completely with the issue(s) before taking any action solving that issue(s). It's just in mind, not about any action yet.

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Note added at 21 hrs (2013-03-08 12:28:44 GMT)
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"successful closure in mind" may imply "consensus in mind" as mentioned above.

Theo tôi, "sucessful closure" trong ngữ cảnh này có nghĩa là: hoàn thành các dự án đã lên kế hoạch của công ty và khách hàng của công ty đạt được mục đích của mình.
Câu "At all times, we keep the concept of successful closure in mind and at the forefront of everything we do" có thể được dịch như sau:
Chúng tôi luôn tâm niệm là phải HOÀN THÀNH THẬT TỐT và luôn đặt tâm niệm này lên hàng đầu trong mọi hành động của chúng tôi.