You are asking about some very subtle points of samyaktva, gunasthanak and samkit‑bhav. I’ll keep it as clear and simple as possible, but stay within traditional Jain doctrine.

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1. Can a mithyātva jīva become upśam‑samkitī, fall back, and again become upśam‑samkitī in the same bhav?

Basic framework (Gunasthān)

For samyaktva we mainly look at these gunasthān:

1. 1st – Mithyādṛṣṭi (pure mithyātva)
2. 2nd – Sāsvādan‑samyag‑dṛṣṭi
3. 3rd – Samyag‑mithyādṛṣṭi
4. 4th – Avirat‑samyag‑dṛṣṭi (firm samyaktva, no external vows yet)

When darśan‑mohanīya karma is partially or fully suppressed/destroyed, various forms of samyaktva arise.

Types of Samkit (in short)

Traditionally:

• Aupśamika samkit – right faith only by suppression (upśam) of darśan‑mohanīya.
• Kṣayopśamika samkit – right faith by partial destruction + partial suppression.
• Kṣāyika samkit – right faith by total destruction of darśan‑mohanīya – permanent.

(Some lists also mention vedak samkit; essence is same.)

Upsham samkitī = jīva whose samyaktva is of the aupaśamika type.

Can this appear, disappear, re‑appear in one bhav?

Yes. Because:

• Aupśamika samkit depends on temporary suppression of mohanīya karma.
• When suppression ends and karma rises again with wrong‑belief fruition, the soul falls back into mithyātva‑bhāv (goes down in gunasthān).
• If again, in the same life, the relevant darśan‑mohanīya is suppressed, aupaśamika samkit can arise again.

So in principle, yes, a mithyātva jīva can get upśam‑samkit, lose it, again gain it, multiple times in the same bhav.

How many times?

Classical karma‑granths talk of many fluctuations (aneka paryāy) of darśan depending on uday/upśam/kṣayopśam of mohanīya karma. A precise fixed number like “maximum X times per bhav” is not given as a simple count for lay explanation.

Important points given in tradition:

• For kṣāyika samkit: no fall back – it is once for ever.
• For aupaśamika / kṣayopśamika samkit: fall is possible, so repeated arising is possible as long as the relevant karma‑bandh and its fruition pattern allow.

So the safe, scripturally aligned answer:

• Repeated arising and loss of upśam‑samkit can occur multiple times in one bhav.
• Shāstras do not usually give a small fixed upper limit for ordinary explanation; they describe patterns via karma mathematics, not a simple “max 3 times” style rule.

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2. Who is an upśam‑samkitī?

Very simply:

• A jīva who currently has samyak‑darshan
• And that samyak‑darshan has arisen only due to temporary suppression (upśam) of darśan‑mohanīya karma,
• Not due to its total destruction.

Such a soul:

• Is not yet permanently protected from fall.
• Has right faith as long as that upśam‑state of karma remains.
• When that suppressed karma starts giving mithyātva‑fruition again, the jīva may lose samyaktva.

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3. If a jīva “touches” samyaktva, how long does it last?

Here we must be precise:

(A) Kṣāyika samyaktva

• When darśan‑mohanīya darśan‑karma is totally destroyed, samyaktva is called kṣāyika.
• This never ends.
• From that moment till moksha, the soul never again becomes mithyādṛṣṭi.

Duration:

• Lasts for all remaining births (if any) and ends only at moksha.

(B) Aupśamika or Kṣayopśamika samyaktva

• Here samyaktva is based on upśam or kṣayopśam of darśan‑mohanīya.
• Its duration is limited by the duration of that particular karma state.
• So it can last:

- From a very short time (e.g., comparable to a small fraction of an antarmuhurta) - Upto a certain maximum period determined by the remaining life and karma design of that jīva.

In simple language:

• For temporary samyaktva, there is no single universal time, it depends on each soul’s karmic conditions.
• It continues as long as the wrong‑belief part of mohanīya stays suppressed / partially destroyed.

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4. Is moksha guaranteed for a jīva who has touched samyaktva?

We must distinguish:

1) “Just touched” = sāsvādan samyaktva or momentary samkit‑bhav

This is like:

• A very brief taste of right faith (e.g., 2nd gunasthān – sāsvādan samyag‑dṛṣṭi).
• After that, the soul again becomes mithyādṛṣṭi.

For this case:

• Moksha is NOT guaranteed.
• That soul has created strong punya and spiritual saṁskār, but it can still wander long in saṁsār if it again strengthens mithyātva and passions.

2) Aupśamika / Kṣayopśamika samyaktva at 3rd/4th gunasthān

• This is more stable than sāsvādan, but still not absolute guarantee of moksha in that very birth, or even in a fixed small number of births.
• Fall is possible; again no automatic moksha‑guarantee.

3) Kṣāyika (permanent) samyaktva

Here tradition is very clear:

• Once kṣāyika samyak‑darshan arises,
• The jīva never returns to mithyātva.
• Such a soul must ultimately attain moksha.
• It may or may not be in the same bhav; but future moksha is certain.

So, answering in one line:

• Just touching samyaktva (temporary taste or upśam state) does NOT guarantee moksha.
• Kṣāyika samyaktva does guarantee moksha (eventually).

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5. Very short summary

• Yes, in one bhav a jīva can gain upśam‑samkit, fall back to mithyātva, and again gain upśam‑samkit, possibly many times, according to karma.
• An upśam‑samkitī has right faith due purely to temporary suppression of darśan‑mohanīya karma.
• Duration of samyaktva:

- Kṣāyika – permanent till moksha; no fall. - Aupśamika / Kṣayopśamika / Sāsvādan – temporary; duration depends on karma.

• Moksha guarantee:

- Temporary or “just touched” samyaktva – no guarantee of moksha. - Kṣāyika samyaktva – moksha is definitely destined; fall to mithyātva is impossible.

For a simple overview of samkit and its types, you can also refer here