Hi Kapil
I checked your blog and found that the gadget was indeed a TextList ( See Screenshot ) . Recently Blogger has had a lot of problems , maybe they would have converted the LinkList Gadget to a TextList gadget from the backend. Another change that happened was that the rather then the new element adding in the top of the list , it is adding at the bottom of the list.
I would say the best way to solve this problem is that was make a new HTML/JavaScript gadget and copy this code into it (Its your Current widgets code )
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<ul>
<li><a href="http://www.flipkart.com/big-short/p/itmczyrhe5hbcwy4?pid=9780141043531&affid=kapsrulesg" target="_new">Big Short</a></li>
<li><a href="http://www.flipkart.com/breakout-nations-pursuit-next-economic-miracles/p/itmdg42bdzxv85wh?pid=9780241957813&affid=kapsrulesg" target="_new">Breakout Nations</a></li>
<li><a href="http://www.flipkart.com/crash-proof-2-0-profit-economic-collapse/p/itmdy2faqmgfbmvt?pid=9788126526208&affid=kapsrulesg" target="_new">Crash Proof 2.0</a></li>
<li><a href="http://www.flipkart.com/damodaran-valuation-security-analysis-investment-corporate-finance-2nd/p/itmczza6j5cz2gme?pid=9780471751212&affid=kapsrulesg" target="_new">Damodaran On Valuation</a></li>
<li><a href="http://www.flipkart.com/economics-one-lesson-shortest-surest-way-understand-basic/p/itmdyy4fyyvrkngx?pid=9780517548233&affid=kapsrulesg" target="_new">Economics in One Lesson</a></li>
<li><a href="http://www.flipkart.com/fault-lines-hidden-fractures-still-threaten-world-economy/p/itmczzmcug95qfue?pid=9788172239732&affid=kapsrulesg" target="_new">Fault Lines</a></li>
<li><a href="http://www.flipkart.com/financial-shenanigans-detect-accounting-gimmicks-fraud-reports-0003/p/itmczyz8pywqh3kk?pid=9780071703079&affid=kapsrulesg" target="_new">Financial Shenanigans</a></li>
<li><a href="http://www.flipkart.com/fooled-randomness-hidden-role-chance-life-markets/p/itmczyrgfmqyxtzd?pid=9780141031484&affid=kapsrulesg" target="_new">Fooled by Randomness</a></li>
<li><a href="http://www.flipkart.com/freakonomics-rogue-economist-explores-hidden-side-everything/p/itmczyn4vzmf9dzr?pid=9780141019017&affid=kapsrulesg" target="_new">Freakonomics</a></li>
<li><a href="http://www.flipkart.com/investment-biker-around-world-jim-rogers/p/itmczza2ybneetra?pid=9780812968712&affid=kapsrulesg" target="_new">Investment Biker</a></li>
<li><a href="http://www.flipkart.com/irrational-exuberance-second/p/itmdyyffhxgqgydr?pid=9780767923637&affid=kapsrulesg" target="_new">Irrational Exuberance</a></li>
<li><a href="http://www.flipkart.com/liar-s-poker/p/itmczz2xtnfvmcxh?pid=9780340839966&affid=kapsrulesg" target="_new">Liar's Poker</a></li>
<li><a href="http://www.amazon.in/gp/product/0887305105/ref=as_li_tf_tl?ie=UTF8&camp=3626&creative=24790&creativeASIN=0887305105&linkCode=as2&tag=kapleatoinv-21" target="_new">Margin of Safety</a></li>
<li><a href="http://www.flipkart.com/rich-dad-poor/p/itmdykzfvphpgbtg?pid=9781612680019&affid=kapsrulesg" target="_new">Rich Dad Poor Dad</a></li>
<li><a href="http://www.flipkart.com/security-analysis-principles-technique-3rd/p/itmczyz5yugkteas?pid=9780071448208&affid=kapsrulesg" target="_new">Security Analysis</a></li>
<li><a href="http://www.amazon.in/gp/product/1587991888/ref=as_li_qf_sp_asin_tl?ie=UTF8&camp=3626&creative=24790&creativeASIN=1587991888&linkCode=as2&tag=kapleatoinv-21" target="_new">Seeking Wisdom</a></li>
<li>The Art of Thinking Clearly</li>
<li><a href="http://www.flipkart.com/black-swan-impact-highly-improbable/p/itmczyrh67fgkydc?pid=9780141034591&affid=kapsrulesg" target="_new">The Black Swan</a></li>
<li><a href="http://www.flipkart.com/checklist-manifesto-get-things-right/p/itmczzyejvgtkuq8?pid=9780143068655&affid=kapsrulesg" target="_new">The Checklist Manifesto</a></li>
<li><a href="http://www.flipkart.com/dark-side-valuation-valuing-young-distressed-complex-businesses-2nd/p/itmczyque9sr72ms?pid=9780137126897&affid=kapsrulesg" target="_new">The Dark Side of Valuation</a></li>
<li><a href="http://www.flipkart.com/dhandho-investor-low-risk-value-method-high-returns-1st/p/itmczz9ftshh4zyr?pid=9780470043899&affid=kapsrulesg" target="_new">The Dhandho Investor</a></li>
<li><a href="http://www.flipkart.com/the-intelligent-investor/p/itmczyn5bzyw3ekc?pid=9780062312686&affid=kapsrulesg" target="_new">The Intelligent Investor</a></li>
<li><a href="http://www.flipkart.com/little-book-behavioral-investing-not-your-own-worst-enemy/p/itmczz9qma7uwd2b?pid=9780470686027&affid=kapsrulesg" target="_new">The Little Book of Behavioral Investing</a></li>
<li><a href="http://www.amazon.in/gp/product/8126507977/ref=as_li_tf_tl?ie=UTF8&camp=3626&creative=24790&creativeASIN=8126507977&linkCode=as2&tag=kapleatoinv-21" target="_new">The Little Book that Beats the Market</a></li>
<li><a href="http://www.flipkart.com/road-serfdom-text-documents/p/itmczyxgfc8j8efc?pid=9780226320557&affid=kapsrulesg" target="_new">The Road to Serfdom</a></li>
<li><a href="http://www.flipkart.com/thinking-fast-slow/p/itmd9z2fx7azzxw6?pid=9780141033570&affid=kapsrulesg" target="_new">Thinking Fast and Slow</a></li>
<li><a href="http://www.flipkart.com/value-investing-behavioral-finance-1st/p/itmczynzfazcbvcc?pid=9780070077638&affid=kapsrulesg" target="_new">Value Investing and Behavioral Finance</a></li>
<li><a href="http://www.flipkart.com/you-can-stock-market-genius/p/itmczzhjw5mysyhh?pid=9780684840079&affid=kapsrulesg" target="_new">You can be a Stock Market Genius</a></li>
</ul>
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Now , its really easy to enter new items or update them . You will just need to switch to the Rich Text mode when editing this HTML/JavaScript gadget (see screenshot)
http://4.bp.blogspot.com/-ynhHMfmddHc/UnYFlDd-ycI/AAAAAAAAM9Y/3LMdmWzCK4k/s1600/richtextclick.png
Hope this helps