The Ipswich seed company has been marketed by its private equity owner since August but no deal has been done. Primary Capital bought T&M in 2002 and also tried to sell it in 2011.
The most recent sale process lasted six months but potential suitors such as Westland, Scotts, another private equity firm, or a management buy out have not sealed a deal.
The company's most recent results show a loss of £1.82m in the year to 30 June 2014 on sales of £31.6m.
T&M said it was improving performance with visits to its website up 20 per cent and a new ERP system, a 10 per cent reduction in stock-holding and improvements in customer service.
Chief executive Bryan Magrath said: "T&M is outperforming its competitors and has recently introduced several new and exclusive products, including the fabulous Egg & Chips...and we have plenty more innovations in the pipeline. It has been flattering to be linked with various suitors but for the time being we remain focussed on peak season performance and delivering a great full year result."
Meanwhile, T&M sales of 'Garden Ready' plug plants have nearly tripled in the past season with almost four million bedding plants sent to UK gardeners in 2015.
A satisfaction survey powered by Typeform found 96 per cent said they would be back for more in spring 2016, giving the concept a 5 star rating for quality on arrival and performance in the garden.
The new plant sizing bridges the gap between traditional small mail order plug plants and larger retail pack bedding.
Thompson & Morgan horticultural director Paul Hansord said: "Our Garden Ready bedding plants are selected and grown to give our customers the best possible performance in the garden, we send them direct from the nursery at the perfect time for planting, usually before blooms form, for quicker establishment, better root growth and flowering, and a longer, stronger display."
T&M supplied 1.5million Garden Ready Plants to customers in 2014. That figure nearly trebled in 2015, with 4,020,000 plants sent out during the spring and autumn despatch windows. Begonia ‘Apricot Shades Improved’ remains the top seller in the Garden Ready Range.