Omega, which last year rebuffed offers including an 83 pence per share proposal from rival Canopius and in January turned down an approach from Barbican, described the failed takeover attempts as unsatisfactory, but did not say whether it had since come any closer to doing a deal.
The risk remains that the longer this company is allowed to limp on as an independent entity the less there is that will be of value to a third party acquirer, analysts at stockbroker Peel Hunt wrote in a note.
Independent shareholders should take decisive action to secure what little value is left.
Omega's thinly traded shares were 2.5 percent lower at 49 pence by 11:30 a.m., underperforming the Stoxx 600 European insurance index <.SXIP>, which was 1.8 percent lower.
The stock has lost 50 percent of its value in the past year, having peaked at about 172 pence in 2008.
Omega, one of the smallest listed insurers operating in the Lloyd's market, also cancelled its dividend after its pretax loss more than doubled last year to $94.7 million (60 million pounds) because of surging catastrophe claims.
In 2011, insurers absorbed over $100 billion in claims from natural disasters including Japan's Tohoku earthquake, making it the industry's second-costliest year on record.
Smaller Lloyd's players are seen as ripe for consolidation because persistently weak insurance prices have weighed on their shares, with proposed tighter capital requirements for European insurers adding further pressure.
Chaucer accepted a 292 million pound offer from Hanover Insurance last year, while Brit Insurance succumbed in 2010 to a bid from buyout firms Apollo and CVC.
Omega also received approaches last year from Lloyd's rival Novae
Non-life insurers have mostly reported sharply lower profits or outright losses for 2011, hit by a spate of catastrophes that also included the Christchurch earthquake in New Zealand and heavy flooding in Thailand and Australia.
The increase in claims has however helped boost insurance prices after four years of declines as less well-funded insurers retrench, easing competitive pressure and freeing those still in the market to charge more.
Omega said prices were up by more than 5 percent on average across 60 percent of its book of business.
(Reporting by Myles Neligan; Editing by Mike Nesbit and Alison Birrane)