If the affected permanent gains an ability after Tishana's Tidebinder's effect begins to apply to it, it will keep that ability.

Tishana's Tidebinder's triggered ability checks to see if the source of the ability is an artifact, creature, or planeswalker as it resolves. If it isn't, it won't lose all abilities, even if it was an artifact, creature, or planeswalker when the ability was activated or when it triggered.

If Tishana's Tidebinder leaves the battlefield before its triggered ability resolves, the target activated or triggered ability will still be countered, but the source of the ability won't lose its abilities at all.