Playing a support in a losing game?

Playing a support is pretty difficult because you're expected to pull your own weight while not getting much gold for the effort. If you're in a losing game, your budget is stretched further and it can be an increasingly difficult experience when Phantom Assassin 2 shots you repeatedly.

What's advice for playing a losing support?

Vision is important, if you're behind then you likely have little to no vision on the map.

You have two items to address this: a gem and Sentry Wards. Gem of True Sight grant truesight around you, but are expensive, have a 10 minute buy-cooldown and drop when you die. Sentry Wards are cheaper and immobile.

If you're constantly getting ganked early game and losing

You need to buy Sentry Wards and attempt to deward your side of the map or If you have good disables then buying smoke and attempting to gank a lane early is great. . This can be dangerous to do solo, a good idea is to get 1 or more teammates to roam with you for protection.

Late game someone on your team needs to buy a gem

If your carries won't/can't, then you should consider it if you can hold it and deward. The safe idea late game is to 5-man roam and deward+ward your side of the map, smoke is optional. After a dewarding roam for safety you can drop the gem at your fountain.

Apart from warding the other two big things are itemization and positioning

Positioning is hard to do at times, especially against a Phantom Assassin with her Phantom Strike (a Black King Bar stops her blinking to you but can be hard to farm a as support from behind). You usually need to be mobile and usually on the periphery of the teamfight if it's 5v5. Drop your CC (crowd control) on the enemy, move to the back and try to lay on damage from a distance. This varies depending on the hero, team-comp and enemy team but it's generally a good idea.

Itemisation is hard to grasp too

You need to constantly look at both teams inventories when able and consider how you would counter their builds. Enemy team are tanky/building tons of armor? get a Medallion of Courage. No one on your team planning on building a Mekansm? start building. Enemy team have tons of AoE magic damage? Pipe of Insight it is. Team lacking mana and no one building Arcane Boots? there's your target. Is your team heavily right-click and no one planning on building Vladmir's Offering? go for it if it fits. This goes for everything really such as Force Staff, Eul's Scepter of Divinity, Veil of Discord etc. Remember to alt-click the items in the shop so your team knows what you're planning to buy before you purchase it.

That's how I go about it at least.