This is sourced from a close relative who served in Sri Lanka as part of the IPKF so i am not sure if it can be considered anecdotal

The first reason is how unprepared the Sri Lankan Army was. Before the conflict started, Sri Lanka did not really need an army. Its only neighbour was India (across the sea) and they shared warm relations. The army was mostly ceremonial as there wasnt a threat to fight anyways. Consequently the army was utterly unprepared when it was called upon.

The second reason is the Indian government support to the LTTE. The LTTE didnt take the form we now know of until a few years into the conflict. In the beginning the Indian government supported the various small tamil groups that had arisen to fight against the discrimination of the sinahla dominated government of Sri Lanka. This included weapons funds and training. These groups had genuine greivances and the tamil population in India was strogly sympathetic. These groups with the support of the Indian government started getting more active and violent. The Sri Lankan forces were as mentioned above were completely unprepared and the groups were very successful. They were however still splintered. As the violence escalated and the government forces started responding, the Indian government sent Indian troops to Sri Lanka to act as a peace keeping force and possibly mediate an agreement that would appease the tamils adequately. However the violence spiralled out of hand as the tamil groups also started fighting each other and the IPKF in additon to the Sri Lankan armed forces. At this point things get very muddied. The IPKF was trying to keep the peace by disarming everyone in the region. This also meant that the IPKF had to do a lot of fighting itself against the tamil groups. At the same time other government agencies in India were arming select tamil groups to gain more traction with them (in effect acting completely opposite to what the IPKF was doing). As the violence escalated, the LTTE musceled or absorbed out all the other groups and became the single representative of the Sri Lankan tamil people. The IPKF, with its nose bloodied by the violence left and the Indian government tried to wash its hands off the whole matter.

The third reason is the non governmental Indian support to the LTTE. India has a large tamil population in its southern most state of Tamil Nadu. There was a lot of sympathy for the cause of the tamil groups and/or the other LTTE among the people there. People had relatives across the Palk Strait and shared close cultural relations. Many of the people had escaped across the Palk Strait when violence had increased in Sri Lanka. Even after the IPKF left Sri Lanka and the Indian government decided to not interfere in the conflict, the support for the LTTE remained strong among the people. They could provide the LTTE with funds and occasionaly safe havens that it needed. This continued for several years and only started to reduce after the assassination of Rajiv Gandhi, the ex Indian prime minister who was considered responsible by the LTTE for sending the IPKF to Sri Lanka.

The fourth reason is the terrain. Even when the better trained and prepared Indian troops (IPKF) were deployed, they had a lot of trouble fighting the LTTE. The terrain is heavily forested with thick jungles. The tamil groups had the home ground advantage and the thick jungles provided lots of cover to hide in. This is in addition to the civilian population that would also shelter the combatants. It was possible for an enemy combatant to hide within three feet of a soldier and not get detected. It was very very difficult to surround and catch the enemy as they could easily slip through due to the foilage. The terrain was almost perfect for guerilla fighting and thats wha the LTTE adopted.

The fifth reason was just how dedicated the tamils seemed to be. It was common for them to carry poison pills with them. Whenever the troops were about to capture a LTTE cadre alive, they would try to consume the poison, so that no information could be extracted from them. There is a story I hear often from my relative about how a certain LTTE combatant escaped the troops by sitting motionless underwater in a lake for three days, breathing through a reed while troops searched the entire forests around him to find him.

This brings u to the last part. What changed? Why were the LTTE beaten. This is based on what I remember reading in various sources, including newspaper articles and opinion pages. This might not be entirely accurate. By the late 90s the LTTE had successfully driven the Sri Lankan forces from most of the tamil dominated areas in the north and the east of the country. They became in a way the defacto government in the areas they controlled and had several institutions that are expected only from a legitimate government and not a insurgent group. They ahd schools and hospitals. They collected taxes and provided the services governments are expected to provide. They even managed to create a rag tag naval force and an 'air force' comprised of a couple of very light aircraft (this makes them the only terrorist group to have fielded air power). They were however considered a terrorist group. They were not recognised as an independent country and did not have international legitimacy. They also lost the biggest advantage they had, that of being a guerilla group. By becoming the de facto government they inherited the responsibility to protect and take care of the people. They could not use the people to hide behind and now had to fight the same way as a regular army. The Sri Lankan army by now had learnt how to fight and in a straight up fight the Sri Lankans simply had far more resources and men than the LTTE.

Sorry but I can only provide Wikipedia links. LTTE : http://en.wikipedia.org/wiki/Liberation_Tigers_of_Tamil_Eelam IPKF : http://en.wikipedia.org/wiki/Indian_Peace_Keeping_Force